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#Random Graphs

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Santa Fe Institute

The Science of Networks - C4 Public Lectures

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Explore the emerging science of networks, their structure, and function across diverse systems. Learn about phase transitions, interdependence, and mathematical models for predicting network behavior and consequences.
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17 Lesons
1 hour 21 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Random Graphs and Nonlinear Spectral Gaps

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Explore discrete Poincaré inequalities in regular expander graphs, long-range expansion properties, and their implications for Banach space-valued functions, with improved estimates for Poincaré constants.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
Institute for Advanced Study

Universality of Random Graphs - Gal Kronenberg

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Explore 2-universality in random graphs, covering monotone properties, age universality, probability thresholds, and expansion properties with proof techniques and examples.
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12 Lesons
1 hour 9 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Ramsey Theory and Random Graphs - Lecture 4

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Explore Ramsey Theory and Random Graphs in this advanced doctoral lecture, delving into complex mathematical concepts and their applications in graph theory.
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1 Lesons
1 hour 27 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Ramsey Theory and Random Graphs - Lecture 3

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Explore Ramsey Theory and Random Graphs in this advanced doctoral lecture, delving into complex mathematical concepts and their applications in graph theory.
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1 Lesons
1 hour 31 minutes
On-Demand
Free-Video
MUNI Seminar Series

The Phase Transition Phenomena in Combinatorial Structures

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Explore phase transitions in combinatorial structures, from physics-inspired concepts to discrete systems, with rigorous analysis of rapid transformations.
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1 Lesons
47 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Clara Stegehuis- Optimization-Based Analysis of Random Graphs I

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Explore random graph models, focusing on power-law degree distributions and optimization-based methods to analyze network properties and underlying geometries.
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1 Lesons
59 minutes
On-Demand
Free-Video
Kyoto-U OCW - Unofficial

Spectrum of Random Graphs - Lecture 1

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Delve into spectral analysis of random graphs, exploring adjacency operators, Laplacian matrices, and Benjamini-Schramm topology. Examine convergence properties and quantum percolation in graph theory.
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1 Lesons
1 hour 55 minutes
On-Demand
Free-Video
Kyoto-U OCW - Unofficial

Spectrum of Random Graphs - Lecture 4

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Delve into advanced spectral analysis of random graphs, exploring adjacency operators, Laplacian operators, and Benjamini-Schramm topology through rigorous mathematical frameworks and quantum percolation theory.
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1 Lesons
2 hours 1 minute
On-Demand
Free-Video
Kyoto-U OCW - Unofficial

Spectrum of Random Graphs - Lecture 2

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Delve into advanced spectral analysis of random graphs, exploring adjacency operators, Laplacian operators, and Benjamini-Schramm topology with focus on spectral measures and quantum percolation theory.
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1 Lesons
2 hours
On-Demand
Free-Video
Kyoto-U OCW - Unofficial

Spectrum of Random Graphs - Lecture 5

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Delve into advanced spectral analysis of random graphs, exploring adjacency operators, Laplacian operators, and Benjamini-Schramm topology through rigorous mathematical frameworks and quantum percolation theory.
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1 Lesons
2 hours 9 minutes
On-Demand
Free-Video
Kyoto-U OCW - Unofficial

Spectrum of Random Graphs - Lecture 3

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Delve into advanced spectral analysis of random graphs, exploring adjacency operators, Laplacian operators, and Benjamini-Schramm topology with focus on convergence properties and quantum percolation.
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1 Lesons
1 hour 56 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Alignment of Random Graphs: Informational and Computational Limits - Lecture 2

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Explores informational and computational limits in aligning random graphs, focusing on advanced probabilistic techniques for data science and graph theory applications.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Alignment of Random Graphs: Informational and Computational Limits - Lecture 1

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Explore informational and computational limits of random graph alignment in this lecture by Laurent Massoulié, part of a data science discussion on probabilistic and optimization methods.
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1 Lesons
48 minutes
On-Demand
Free-Video
Society for Industrial and Applied Mathematics

Random Monomial Ideals - Seminar on Applied Geometry and Algebra

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Explore probabilistic models of random monomial ideals, their properties, and applications in algebraic geometry. Gain insights into average behavior of ideals and potential for generating algebraic objects.
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1 Lesons
46 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Spectrum of Sparse Inhomogeneous Random Graphs

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Explore the spectrum of sparse inhomogeneous random graphs, examining structural properties and applications in network science, probability theory, and statistical physics.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
International Centre for Theoretical Sciences

Path Convergence of Markov Chains on Large Graphs

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Explore path convergence of Markov chains on large graphs, examining theoretical aspects and applications in network science, probability theory, and complex systems analysis.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Algorithms on Networks

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Explore algorithms for network analysis, optimization, and control. Learn techniques for solving complex problems on graphs and networks, with applications in various fields.
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1 Lesons
53 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Best Arm Identification Through Fluid-Based Methods

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Explore fluid-based methods for best arm identification in multi-armed bandit problems. Learn innovative techniques to optimize decision-making in uncertain environments.
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1 Lesons
52 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Well Posedness for Hamilton-Jacobi Equations for Linearly Controlled Gradient Flows

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Explore well-posedness of Hamilton-Jacobi equations for linearly controlled gradient flows, examining mathematical foundations and applications in optimization and control theory.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Asymptotics of Invariant Measures of Mean-field Markov Models on Countable State Spaces

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Explore asymptotics of invariant measures in mean-field Markov models on countable spaces. Gain insights into network science, probability theory, and applications in complex systems and data analysis.
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1 Lesons
52 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

The Friendship Paradox for Sparse Random Graphs

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Explore the friendship paradox in sparse random graphs, examining structural properties and implications for network analysis and social dynamics.
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1 Lesons
53 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Eulerian Magnitude Homology - Subgraph Structure and Random Graphs

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Explore connections between magnitude homology group ranks and graph substructures. Introduces eulerian and discriminant magnitude homology, relating them to subgraph counts and random graph models.
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1 Lesons
47 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

The Random Friend Tree by Serte Donderwinkel

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Explore the Random Friend Tree model in network science, examining its structural properties, dynamics, and applications in social networks and complex systems.
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1 Lesons
1 hour 16 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Scaling Exponents in Stationary Random Graphs

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Explore scaling exponents in stationary random graphs, examining relationships between fractal dimension, walk dimension, resistance, spectral dimension, and extremal growth in statistical physics.
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1 Lesons
55 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Sharp Threshold for Rigidity of Random Graphs

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Explore the evolution of random graphs and discover key moments when they become rigid and globally rigid, with implications for vertex embedding and distance preservation.
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1 Lesons
52 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Graph Limit for Interacting Particle Systems on Weighted Deterministic and Random Graphs

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Explore graph limits for interacting particle systems on weighted deterministic and random structures in this advanced mathematical lecture.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
Institute for Advanced Study

Spectral Gap of the Laplacian for Random Hyperbolic Surfaces

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Explore spectral gap of Laplacian for random hyperbolic surfaces in large genus limit. Delve into Weil-Petersson measure, Mirzakhani's work, and trace method applications.
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1 Lesons
1 hour 12 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Interacting Particle Systems on Sparse W-Random Graphs

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Explore interacting particle systems on sparse W-random graphs in this workshop. Gain insights from leading experts through plenary talks, contributed presentations, and collaborative sessions on randomness and network learning.
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1 Lesons
16 minutes
On-Demand
Free-Video
Institute for Advanced Study

A New Approach to Strong Convergence - Lecture 1

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Explore a novel approach to strong convergence in graph theory, addressing Alon's conjecture and extending Friedman's theorem with applications to random graphs, geometry, and operator algebras.
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1 Lesons
2 hours 7 minutes
On-Demand
Free-Video
Institute for Advanced Study

Spectral Gap of the Laplacian for Random Hyperbolic Surfaces - Part 2

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Explore spectral gap of Laplacian for random hyperbolic surfaces using trace method and asymptotic expansions in large genus limit. Analyze Weil-Petersson measure and Friedman-Ramanujan property.
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1 Lesons
1 hour 7 minutes
On-Demand
Free-Video
Banach Center

The K-Distribution of Random Graph C*-Algebras

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Explore the K-distribution of random graph C*-algebras, delving into advanced mathematical concepts and their applications in algebraic structures.
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1 Lesons
1 hour 9 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Towards an Optimal Spectral Gap Result for Random Compact Hyperbolic Surfaces

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Explore recent progress in proving near-optimal spectral gaps for hyperbolic surfaces. Delve into trace methods, challenges, and new tools developed to improve bounds in spectral geometry.
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1 Lesons
1 hour 11 minutes
On-Demand
Free-Video
BIMSA

The Chromatic Number of Random Graphs

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Explore the chromatic number of random graphs, focusing on lower bounds for G(n,1/2) and its limiting distribution. Discover recent advancements in graph theory and probabilistic methods.
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1 Lesons
46 minutes
On-Demand
Free-Video
BIMSA

Canonical Colourings in Random Graphs

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Explore canonical colourings in random graphs with Nina Kamčev, delving into extremal combinatorics, Ramsey theory, and asymptotic enumeration.
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1 Lesons
51 minutes
On-Demand
Free-Video
BIMSA

Partitioning a Tournament into Sub-Tournaments of High Connectivity

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Explore tournament partitioning techniques to create highly connected sub-tournaments, delving into extremal and probabilistic combinatorics, Ramsey theory, and random graphs.
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1 Lesons
1 hour 8 minutes
On-Demand
Free-Video
BIMSA

Simonovits's Theorem in Random Graphs

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Explore Simonovits's theorem in random graphs with Wojciech Samotij. Gain insights into extremal and probabilistic combinatorics from an award-winning mathematician.
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1 Lesons
57 minutes
On-Demand
Free-Video
BIMSA

Structures Robust Under Randomness - Probabilistic Combinatorics and Thresholds

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Explore robustness of discrete system substructures under random subsampling, examining thresholds in random graphs and key conjectures in probabilistic combinatorics.
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1 Lesons
54 minutes
On-Demand
Free-Video
PCS Institute for Basic Science

Global Synchronization: New Theorems and Puzzles in Kuramoto Oscillator Networks

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Explore global synchronization in Kuramoto oscillator networks, examining critical connectivity thresholds and unsolved puzzles in network behavior.
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14 Lesons
53 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Discrete Random Models - Minicourse 03

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Explore discrete random models in this advanced mathematics workshop. Gain insights into probabilistic techniques for analyzing complex network structures and random processes.
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1 Lesons
1 hour 13 minutes
On-Demand
Free-Video
Simons Institute

Structures in Random Graphs - New Connections

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Exploring structures in random graphs, including cliques and independence numbers in Cayley graphs, thresholds for monotone properties, and edge-colorings of bipartite graphs.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
ACM SIGPLAN

Probabilistic Programming Interfaces for Random Graphs: Markov Categories, Graphons, and Nominal Sets - POPL 2024

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Explore semantic models of probabilistic programming languages over graphs, connecting graphons to equational theories through Markov categories, measure-theoretic probability, and nominal sets.
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1 Lesons
19 minutes
On-Demand
Free-Video
IEEE

Optimization of the Sherrington-Kirkpatrick Hamiltonian

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Explore the optimization of the Sherrington-Kirkpatrick Hamiltonian, covering stochastic block models, random graphs, and algorithmic insights for solving complex optimization problems.
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16 Lesons
23 minutes
On-Demand
Free-Video
IEEE

Fast Uniform Generation of Random Graphs with Given Degree Sequences

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Explore efficient algorithms for generating random graphs with specified degree sequences, focusing on rejection and switching methods.
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14 Lesons
20 minutes
On-Demand
Free-Video
Joint Mathematics Meetings

Interacting Stochastic Processes on Random Graphs

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Explore interacting stochastic processes on random graphs, covering models like voter and neuronal hox, and examining challenges in sparse regimes and local convergence.
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25 Lesons
1 hour 11 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

The Largest Common Subtree of Uniform Attachment Trees

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Explore the largest common subtree of uniform attachment trees in this advanced mathematics workshop, featuring expert talks and collaborative sessions on network analysis and discrete probability.
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1 Lesons
58 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Statistical Network Analysis - Course 2

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Explore statistical network analysis techniques with experts from Texas A&M and Wisconsin. Gain insights into discrete probability, collaborate on open problems, and advance your research in this month-long program.
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1 Lesons
1 hour 22 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Statistical Network Analysis - Course 2

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Explore statistical network analysis techniques with experts from Texas A&M and Wisconsin. Gain insights into discrete probability, collaborate on open problems, and advance your research in this month-long program.
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1 Lesons
1 hour 22 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Statistical Network Analysis - Course 2

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Explore statistical network analysis techniques with experts from Texas A&M and Wisconsin. Gain insights into discrete probability, collaborate on open problems, and advance your research in this month-long program.
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1 Lesons
1 hour 29 minutes
On-Demand
Free-Video
MIT OpenCourseWare

Threshold for a Random Graph to Contain a Triangle - MIT 18.226

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Explore probabilistic methods to determine when random graphs develop triangles, using first and second moment analysis techniques in combinatorial mathematics.
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1 Lesons
29 minutes
On-Demand
Free-Video
MIT OpenCourseWare

Bounded Differences Inequality and Azuma-Hoeffding Inequality

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Master probabilistic analysis through the Bounded Differences Inequality, exploring its applications in coupon collection and random graph coloring, with focus on Lipschitz functions and concentration bounds.
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1 Lesons
20 minutes
On-Demand
Free-Video