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#Random Matrix Theory

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Centre de recherches mathématiques - CRM

The Moduli Space of Twisted Laplacians and Random Matrix Theory

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Explore the convergence of spectral number variance for twisted Laplacians to random matrix theory ensembles, extending Rudnick's work to break time-reversal symmetry and include Dirac operators.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

The Mathematics of Scaling Laws and Model Collapse in AI

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Explore the mathematics behind AI scaling laws and model collapse, focusing on the shift from linear to flattened performance relationships in large language models.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
Institute for Advanced Study

An Introduction to Determinantal Point Processes - John C Urschel

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Explore determinantal point processes: definition, examples, and applications in random matrix theory, combinatorics, and machine learning. Survey key results and open questions.
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13 Lesons
2 hours 10 minutes
On-Demand
Free-Video
Institut Henri Poincaré

Un Petit Aperçu des Matrices de Wigner

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Explorez les matrices de Wigner et leurs applications en mathématiques avancées avec Sandrine Dallaporta de l'Université de Poitiers.
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1 Lesons
2 hours 28 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Spectrum of Random Quantum Channels

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Explore the spectrum of random quantum channels in this advanced mathematical talk by Cécilia Lancien, delving into complex concepts and recent research findings.
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1 Lesons
45 minutes
On-Demand
Free-Video
ICTP Mathematics

On Spectra of Quasiperiodic Matrices

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Explore the mathematical intricacies of quasiperiodic matrices and their spectral properties in this advanced lecture by Igor Krasovsky from Imperial College London.
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1 Lesons
46 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Time and Band Limiting for Exceptional Orthogonal Polynomials

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Explore time-and-band limiting in exceptional orthogonal polynomials, connecting integral operators, differential equations, and bispectral problems. Uncover links to KdV equations and random matrix theory.
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1 Lesons
57 minutes
On-Demand
Free-Video
Alan Turing Institute

Mathematical Representations and Models - Professor Jared Tanner, Oxford University

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Explore mathematical models for high-dimensional data analysis with Oxford's Prof. Tanner. Learn about Fourier series, localisation, coherence, and advanced techniques for efficient information extraction and processing.
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12 Lesons
53 minutes
On-Demand
Free-Video
Simons Semester on Dynamics

Estimating Dimension and Lyapunov Exponents - Lecture 2A

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Explore advanced mathematical concepts in dimension theory, including Hausdorff dimensions, Lyapunov exponents, and their applications to number theory and geometric systems.
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1 Lesons
51 minutes
On-Demand
Free-Video
Simons Semester on Dynamics

Estimating Dimension and Lyapunov Exponents - Lecture 2B

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Explore advanced mathematical concepts in dimension theory, including Hausdorff dimensions, Lyapunov exponents, and their applications to number theory and geometric systems.
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1 Lesons
44 minutes
On-Demand
Free-Video
Simons Semester on Dynamics

Estimating Dimension and Lyapunov Exponents - Lecture 1A

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Explore advanced mathematical concepts of Hausdorff dimension, Lyapunov exponents, and their applications in dynamical systems and number theory through detailed theoretical analysis.
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6 Lesons
37 minutes
On-Demand
Free-Video
Simons Institute

Finding Low-Rank Matrices - From Matrix Completion to Recent Trends

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Explore low-rank matrix recovery, from matrix completion to recent trends, covering theoretical foundations and applications in signal processing and machine learning.
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23 Lesons
54 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Random Matrix Theory and its Applications - Lecture 4

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Explore advanced concepts in Random Matrix Theory, including rotational invariance, correlation functions, spacing distributions, and applications to complex systems stability.
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16 Lesons
1 hour 33 minutes
On-Demand
Free-Video
International Mathematical Union

Weingarten Calculus and Its Applications

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Explore Weingarten calculus and its applications in compact groups, quantum probability, and random matrix theory, with insights on theoretical properties and recent developments.
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22 Lesons
46 minutes
On-Demand
Free-Video
ICTP Mathematics

Large Deviations for Traces of Wigner Matrices

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Large deviations theory for traces of Wigner matrices, exploring typical behaviors, principles, and universality. Covers bounded and sub-Gaussian entries, mechanisms, and nonlinear aspects of random matrix theory.
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15 Lesons
44 minutes
On-Demand
Free-Video
ICTP Mathematics

Asymptotics of the Averaged Characteristic Polynomial for Ginibre Ensemble

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Explore asymptotics of averaged characteristic polynomials in Ginibre Ensemble, covering Coulomb gas, Szego curves, orthogonal polynomials, and partition functions in random matrix theory.
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5 Lesons
35 minutes
On-Demand
Free-Video
ICTP Mathematics

Determinantal Point Processes - V

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Explore determinantal point processes, covering conditional measures, sign processes, gamma kernels, Palm measures, and infinite determinantal measures in this advanced mathematics lecture.
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6 Lesons
1 hour 3 minutes
On-Demand
Free-Video
ICTP Mathematics

Absolute Continuity of Limiting Spectral Distributions of Toeplitz and Hankel Random Matrices

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Explore limiting spectral distributions of Toeplitz and Hankel matrices, focusing on absolute continuity and its implications for random matrix theory.
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7 Lesons
40 minutes
On-Demand
Free-Video
ICTP Mathematics

Eigenvalue Distribution for Non Linear Models of Random Matrices

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Explore eigenvalue distribution in non-linear random matrix models, covering motivation, limits, batch normalization, and moment methods with speaker Sandrine PECHE.
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13 Lesons
43 minutes
On-Demand
Free-Video
ICTP Mathematics

Random Matrices and the Uses of Dyson-Schwinger Equations - III

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Explore advanced topics in random matrix theory, including Dyson-Schwinger equations, operator algebra, and central limit theorems, with applications in mathematical physics.
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12 Lesons
1 hour
On-Demand
Free-Video
ICTP Mathematics

Edge Universality for Non-Hermitian Random Matrices

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Explore edge universality in non-Hermitian random matrices, covering eigenvalues, circular law, universality conjectures, and proof techniques for spectral universality and Girko's Hermitization.
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12 Lesons
49 minutes
On-Demand
Free-Video
ICTP Mathematics

Determinantal Point Processes - II

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Exploration of determinantal point processes, covering theorems, Young graphs, Markov chains, and related mathematical concepts with applications in random matrix theory.
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11 Lesons
57 minutes
On-Demand
Free-Video
ICTP Mathematics

Variational Problems and Spectral Curves for the Hermitian Matrix Model with External Source

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Explore variational problems and spectral curves in hermitian matrix models with external sources, focusing on finite N spectral curves and their applications in random matrix theory.
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9 Lesons
44 minutes
On-Demand
Free-Video
ICTP Mathematics

Color-Position Symmetry in Interacting Particle Systems

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Explore color-position symmetry in particle systems, covering probability, partition functions, and stochastic processes. Gain insights into ASEP and simulation techniques.
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12 Lesons
38 minutes
On-Demand
Free-Video
ICTP Mathematics

Random Matrices and the Uses of Dyson-Schwinger Equations - I

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Explore random matrices, matrix models, and Dyson-Schwinger equations in this advanced mathematics lecture, focusing on integration techniques and unique solutions.
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11 Lesons
1 hour
On-Demand
Free-Video
International Centre for Theoretical Sciences

Random Matrix Theory and Its Applications - Lecture 3

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Explore advanced random matrix theory concepts, including complex quaternionic matrices, rotationally invariant ensembles, and applications to disordered systems in this in-depth lecture.
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17 Lesons
1 hour 32 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Random Matrix Theory and Its Applications - Lecture 5

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Explore advanced random matrix theory concepts, including Gaussian ensembles, coarse-graining techniques, and the Wigner semi-circular law in this comprehensive lecture.
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15 Lesons
1 hour 24 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Random Matrix Theory and its Applications - Lecture 2

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Explore advanced concepts in random matrix theory, including linear algebra basics, operators, transformations, eigenvectors, and various matrix ensembles, with applications in statistical physics.
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21 Lesons
1 hour 28 minutes
On-Demand
Free-Video
International Mathematical Union

Quantitative Invertibility of Non-Hermitian Random Matrices

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Explore quantitative invertibility of non-Hermitian random matrices with Konstantin Tikhomirov in this mathematical lecture on advanced linear algebra concepts.
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1 Lesons
43 minutes
On-Demand
Free-Video
ICTP Mathematics

Noise Sensitivity of the Top Eigenvector of a Wigner Matrix

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Explore the noise sensitivity of Wigner matrices' top eigenvectors, delving into random matrix theory and its applications in mathematical physics and data analysis.
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1 Lesons
41 minutes
On-Demand
Free-Video
ICTP Mathematics

Determinantal Point Processes - Lecture 3

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Explore advanced concepts in determinantal point processes, focusing on mathematical theory and applications in random matrix theory and point processes.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
ICTP Mathematics

Christoffel Deformations of Discrete Ensembles

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Explore Christoffel deformations in discrete ensembles, examining their mathematical properties and applications in random matrix theory and point processes.
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1 Lesons
46 minutes
On-Demand
Free-Video
ICTP Mathematics

Local Eigenvalue Statistics for Band Matrices With a Transfer Operator Approach

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Explore local eigenvalue statistics for band matrices using transfer operator methods, presented by Maria Shcherbina from ILTP, Kharkov, Ukraine.
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1 Lesons
39 minutes
On-Demand
Free-Video
ICTP Mathematics

Random Matrices and the Uses of Dyson-Schwinger Equations - Lecture 2

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Explore advanced concepts in random matrix theory, focusing on Dyson-Schwinger equations and their applications in mathematical physics and statistical mechanics.
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1 Lesons
54 minutes
On-Demand
Free-Video
ICTP Mathematics

Determinantal Point Processes - Lecture 1

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Explore determinantal point processes with Alexander Bufetov, delving into mathematical concepts and applications in random matrix theory.
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1 Lesons
1 hour
On-Demand
Free-Video
ICTP Mathematics

Random Matrices and the Uses of Dyson-Schwinger Equations - Lecture 5

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Explore advanced concepts in random matrix theory, focusing on Dyson-Schwinger equations and their applications in mathematical physics and probability theory.
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1 Lesons
54 minutes
On-Demand
Free-Video
ICTP Mathematics

The Point Processes at Turning Points of Large Lozenge Tilings

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Explore the fascinating world of point processes in large lozenge tilings, focusing on turning points and their mathematical implications.
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1 Lesons
43 minutes
On-Demand
Free-Video
ICTP Mathematics

Random Matrices and the Uses of Dyson-Schwinger Equations - Lecture 4

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Explore advanced concepts in random matrix theory, focusing on Dyson-Schwinger equations and their applications in mathematical physics and probability theory.
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1 Lesons
56 minutes
On-Demand
Free-Video
Fields Institute

On the X Y Symmetry in Topological Recursion via Loop Insertion Operator

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Explore the x-y symmetry in Topological Recursion through the lens of loop insertion operators, delving into advanced mathematical concepts and their applications.
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1 Lesons
59 minutes
On-Demand
Free-Video
Fields Institute

Third Order Cumulants of Complex Wigner Matrices

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Explore third order cumulants of complex Wigner matrices in noncommutative geometry and free probability theory, advancing understanding of random matrix theory.
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1 Lesons
1 hour 11 minutes
On-Demand
Free-Video
Fields Institute

Homological Methods in Random Noncommutative Geometry

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Explore homological methods in random noncommutative geometry, covering fuzzy spectral triples, Dirac operators, and connections to random matrix theory and BV formalism.
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21 Lesons
53 minutes
On-Demand
Free-Video
Fields Institute

How Topological Recursion Organizes Quantum Fields on Noncommutative Geometries - Part 2

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Explore advanced concepts in quantum field theory, focusing on topological recursion and its application to noncommutative geometries in this advanced mathematics lecture.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
Fields Institute

Delocalization of Eigenvectors of Large Random Matrices

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Explore eigenvector delocalization in large random matrices, examining mathematical concepts and implications for probability theory and matrix analysis.
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1 Lesons
53 minutes
On-Demand
Free-Video
Fields Institute

Consequences of the Random Matrix Solution to the Peterson-Thom Conjecture

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Explore the implications of random matrix theory in solving the Peterson-Thom conjecture, presented by Benjamin Hayes from the University of Virginia.
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1 Lesons
50 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Random Matrix Statistics in the Uniform Spanning Tree

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Explore random matrix statistics in uniform spanning trees, focusing on branch behavior, scaling limits, and connections to Dyson Brownian motion and Loewner evolution.
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1 Lesons
51 minutes
On-Demand
Free-Video
USC Probability and Statistics Seminar

Spectral Stability Under Real Random Absolutely Continuous Perturbations

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Explore spectral stability in random matrix perturbations, focusing on eigenvector condition numbers and minimum eigenvalue gaps. Gain insights into numerical linear algebra algorithms.
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17 Lesons
47 minutes
On-Demand
Free-Video
Fields Institute

Graphs of Random Matrices in Deep Learning

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Explore the intersection of random matrix theory and deep learning, focusing on graph structures and their implications for neural network performance and analysis.
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1 Lesons
25 minutes
On-Demand
Free-Video
Isaac Newton Institute for Mathematical Sciences

Disordered Systems and Related Spectra - Rothschild Lecture

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Explore disordered systems and spectral theory, focusing on Schrodinger operators with random potential and large random matrices.
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1 Lesons
1 hour 12 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Shuffling Cards and Random Matrix Theory

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Explore card shuffling and random matrix theory with Stanford's Persi Diaconis in this IMPA 70th anniversary conference talk on mathematical applications in everyday phenomena.
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1 Lesons
1 hour
On-Demand
Free-Video
ICTP-SAIFR

Random Matrix Theory Applications from Single to Many-Body Quantum Chaos - Class 2

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Explore random matrix theory applications in quantum chaos, from single-particle to many-body systems, with insights from Thomas Guhr's advanced lecture series.
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1 Lesons
1 hour 42 minutes
On-Demand
Free-Video
IPhT-TV

On the Integrability of the Airy Kernel and Beyond

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Explore integrability of the Airy kernel and related mathematical concepts in this advanced mathematical analysis presentation by Sofia Tarricone.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
Schmid College, Chapman University

Linear Systems and Differential Equations in Random Matrix Theory

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Explore linear systems and differential equations in random matrix theory, focusing on solving nonlinear equations using Hankel operators, Fredholm determinants, and tau functions.
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20 Lesons
50 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Outliers of Perturbations of Banded Toeplitz Matrices

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Explore outlier eigenvalues of perturbed banded Toeplitz matrices, focusing on their behavior in regions outside the limiting spectral distribution's support as matrix size increases.
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1 Lesons
54 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Sums of the Divisor Function and Random Matrix Distributions - Lecture

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Explore divisor function behavior, distribution strategies, and connections to Riemann zeta function and random matrix groups in number theory.
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1 Lesons
1 hour 7 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Ensembles of Random Matrices with Complex Potentials - Workshop on Integrable Systems

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Explorez les résultats rigoureux récents sur l'expansion topologique et le diagramme de phase dans les ensembles de matrices aléatoires avec potentiels complexes cubiques et quartiques.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
BIMSA

Recent Progress in Random Matrix Theory

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Explore recent advancements in random matrix theory, focusing on spectral statistics of normalized adjacency matrices in random d-regular graphs and their eigenvalue rigidity.
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1 Lesons
1 hour
On-Demand
Free-Video
BIMSA

The KPZ Fixed Point - Understanding Random Growing Interfaces

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Explore the KPZ universality class, its fixed point, and connections to random matrix theory and integrable systems in growing interfaces and exclusion processes.
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1 Lesons
51 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Branching Processes in Random Matrix Theory and Analytic Number Theory

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Explore branching processes in random matrix theory and analytic number theory, focusing on limiting distributions, log-correlated phenomena, and recent conjectures about maxima of characteristic polynomials and L-functions.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
International Centre for Theoretical Sciences

Random Matrix Theory and Its Applications by Satya Majumdar

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Explore Random Matrix Theory's foundations and applications in physics, mathematics, and data science. Learn key concepts and techniques from expert Satya Majumdar.
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1 Lesons
1 hour 23 minutes
On-Demand
Free-Video
International Mathematical Union

Convergence of the Two-Point Form Factor Series in the 1+1 Dimensional Sinh-Gordon Model

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Explores convergence of form factor series in 1+1D Sinh-Gordon model, developing techniques to prove convergence and estimate large-n behavior of n-fold integrals, advancing mathematical foundations of integrable quantum field theories.
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1 Lesons
48 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Quantum Phases of Matter - The SYK Model

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Explore quantum phases of matter through the SYK model with Prof. Sachdev. Delve into free fermion systems, entropy, random matrices, and complex quantum phenomena in this advanced theoretical physics lecture.
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15 Lesons
1 hour 32 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Fractionalized Metallic Phases in the Single Band Hubbard Model - Quantum Phases of Matter XXII

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Explore fractionalized metallic phases in the single band Hubbard model, covering pseudogap regimes, photoemission experiments, and strange metal behavior. Gain insights into quantum phases of matter from expert Subir Sachdev.
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31 Lesons
1 hour 35 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Quantum Aspects of Black Holes - Lecture 3

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Explore quantum aspects of black holes, including traversable wormholes, quantum teleportation, and the Hayden-Preskill problem. Delve into chaotic systems, random matrices, and gravity solutions for the ramp.
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33 Lesons
1 hour 50 minutes
On-Demand
Free-Video
ICTP Mathematics

Soliton Quantization and Random Partitions

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Explore soliton quantization and random partitions in Benjamin Ono equations, focusing on one-phase solutions, simulations, and Hamiltonian structures in dispersive wave theory.
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16 Lesons
44 minutes
On-Demand
Free-Video
Fields Institute

Tensor Harish-Chandra–Itzykson–Zuber Integral & Entanglement Detection in Multipartite Quant Systems

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Explore tensor integrals and their applications in quantum entanglement detection, focusing on multipartite systems and advanced mathematical concepts in quantum physics.
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1 Lesons
43 minutes
On-Demand
Free-Video
Fields Institute

How Topological Recursion Organizes Quantum Fields on Noncommutative Geometries - Part 3

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Explore advanced concepts in quantum field theory and noncommutative geometry, focusing on topological recursion and its applications in organizing quantum fields.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
Fields Institute

Quantum Gravity From Integration Over Dirac Ensembles

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Explore the intersection of quantum gravity and Dirac ensembles in this advanced physics lecture, delving into cutting-edge theories and mathematical frameworks.
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1 Lesons
52 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Sums of GUE Matrices and Concentration of Hives from Correlation Decay of Eigengaps

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Explore the concentration of augmented hives in sums of random Hermitian matrices, using GUE ensemble eigenvalues and analyzing asymptotic behavior as eigenvalue count increases.
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1 Lesons
48 minutes
On-Demand
Free-Video
Kavli Institute for Theoretical Physics

Living in the Matrix - Recent Advances in Understanding Quantum Spacetime

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Explore recent advances in quantum gravity, including "random matrix" models for spacetime emergence, and their implications for understanding black holes and the universe's origins.
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1 Lesons
1 hour 11 minutes
On-Demand
Free-Video
Simons Institute

Emergence of Universal Randomness in Quantum Many-body Dynamics

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Explore universal randomness in quantum dynamics, deep thermalization, and Hilbert-space ergodicity. Learn about applications in quantum information theory and experimental observations.
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1 Lesons
44 minutes
On-Demand
Free-Video
Galileo Galilei Institute

Examples of Resurgence Effects in JT Gravity - Spectral Form Factor and Weyl-Petersson Volumes

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Explore resurgence effects in JT gravity, focusing on Spectral Form Factor and Weyl-Petersson Volumes. Gain insights into advanced theoretical physics concepts and their applications.
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1 Lesons
1 hour 25 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Quantum Exclusion Process, Random Matrices and Free Cumulants

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Explore quantum exclusion process, random matrices, and free cumulants in relation to particle hopping models and their invariant measure fluctuations.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

A Statistical Physics Approach to the Sine Beta Process and Other Random Point Processes

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Explore statistical physics approaches to Sine Beta processes and random point systems, focusing on universality properties and applications of DLR tools.
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1 Lesons
54 minutes
On-Demand
Free-Video
Galileo Galilei Institute

Tracy-Widom Distribution in Four-Dimensional Super-Yang-Mills Theories

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Explore the Tracy-Widom distribution in super-Yang-Mills theories, examining its applications and implications in theoretical physics and mathematical modeling.
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1 Lesons
53 minutes
On-Demand
Free-Video
Fields Institute

Bipartite Spherical Spin Glass at Critical Temperature - With a Random Matrix Detour

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Explore the intricacies of bipartite spherical spin glass at critical temperature, including insights from random matrix theory in this advanced probability seminar.
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1 Lesons
49 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Entanglement Detection in Quantum Information Theory: A Random Matrix Theory Approach

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Explore entanglement detection in quantum information theory using random matrix theory. Gain insights into advanced mathematical approaches for quantum systems analysis.
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1 Lesons
39 minutes
On-Demand
Free-Video
ICTP-SAIFR

Semiclassical Theory Approach in Quantum Chaos - Class 1

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Explore semiclassical theory in quantum chaos with Martin Sieber, focusing on foundational concepts and applications in complex quantum systems.
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1 Lesons
1 hour 28 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Random Tensor Networks with Nontrivial Links

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Explorez les réseaux de tenseurs aléatoires avec états de liens non triviaux, leurs propriétés d'intrication et applications en théorie de l'information quantique et gravité quantique holographique.
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21 Lesons
1 hour
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Deep Learning, Correlations, and the Statistics of Natural Images

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Explore how Deep Neural Networks leverage statistical patterns in natural images and diverse datasets, examining their remarkable ability to identify and utilize robust correlational structures.
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1 Lesons
42 minutes
On-Demand
Free-Video