Order and Patterns in Randomness by Abhishek Dhar
Explore hidden patterns in seemingly random events through examples of Random Walk, Brownian Motion, Statistical Physics, and a card trick. Gain insights into physicists' and mathematicians' approaches.
Random Walks on Hyperbolic Groups by Peter Haissinsky
Explore random walks on hyperbolic groups in this lecture by Peter Haissinsky, covering fundamental concepts, techniques, and applications in geometric group theory and probability.
Probabilistic Generative Frameworks for Sampling 3D Complex Shapes and Images
Explore probabilistic frameworks for simulating 2D and 3D shapes, with applications in computational biology. Learn about sub-image selection and shape statistics in cellular imaging and primate mandibular molars.
Introduction to Stochastic Processes by Sanjib Sabhapandit
Explore stochastic processes in this advanced lecture, covering key concepts and applications in statistical physics for graduate-level students and researchers.
Introduction to the Normal Distribution and Continuous Random Variables
Explore continuous random variables and the normal distribution, key concepts in statistical analysis for understanding data patterns and probability distributions.
A Study of Probability Distributions, Mean, and Standard Deviation
Explore probability distributions, mean, and standard deviation in this comprehensive lecture on fundamental statistical concepts.
Probability Theory for Random Groups Arising in Number Theory
Explores probability theory for random groups in number theory, topology, and combinatorics. Covers moment problems, universality theorems, and distributions of class groups and Selmer groups.
Hydrodynamic Limit and Stochastic PDEs Related to Interface Motion
Explore interacting particle systems and their macroscopic behavior through hydrodynamic limits, deriving models for interface motion in phase separation, species segregation, and coupled KPZ equations.
Alice Guionnet: Random Matrices, Free Probability and the Enumeration of Maps
Explore connections between random matrices, free probability, and map enumeration in this advanced mathematical lecture by renowned expert Alice Guionnet.
Keith Ball- The Probabilistic Character of Convex Domains
Explore the probabilistic nature of convex domains with mathematician Keith Ball, delving into geometric concepts and their applications in probability theory.
Stochastic Topology and Statistical Persistence
Explore stochastic topology and statistical persistence, delving into advanced mathematical concepts and their applications in data analysis and machine learning.
Mixing Time and Cutoff for One Dimensional Particle Systems
Explores quantitative aspects of Markov chain convergence, focusing on mixing time and cutoff phenomenon in simple exclusion processes and random walks on the simplex.
Patricia Gonçalves- On Hydrodynamic Limits of Fractional PDEs From Stochastic Interacting
Explores hydrodynamic limits of fractional PDEs derived from stochastic interacting particle systems, focusing on recent advances in scaling limit procedures and boundary conditions.
Hammond and Sheffields Power Law Pólya's Urn
Explores power law Pólya's urn model, analyzing genealogical aspects, coalescence probabilities, and asymptotic behavior. Discusses random partitions, fractional Brownian motion, and metastable systems in probability theory.
Stochastic Ricci Flow on Surfaces
Explores stochastic Ricci flow in 2D, introducing its formulation, symmetry properties, and construction of weak solutions. Discusses implications for compact surfaces and open questions.
Concentration Functions and Entropy Bounds for Discrete Log-Concave Distributions
Explore concentration functions and entropy bounds for discrete log-concave distributions, with applications to entropy power inequalities. Based on joint research in probability theory.
Stochastic Analysis and Geometric Functional Inequalities
Explore methods for proving functional inequalities in hypoelliptic diffusions, including geometric and probabilistic approaches, with applications to Langevin dynamics ergodicity.
Schramm-Steif Variance Inequalities for Poisson Processes and Noise Sensitivity
Explore Poisson processes, variance inequalities, and noise sensitivity in stochastic geometry. Gain insights into k-percolation and the Poisson Boolean model with bounded grains.
The Large Deviations Approach to High-Dimensional Convex Bodies - Lecture I
Explores large deviation principles in high-dimensional convex bodies, focusing on non-universal behaviors in random projections and their relation to underlying geometry.
Functional Inequalities and Concentration of Measure III
Explores concentration inequalities in probability and geometric analysis, focusing on functional inequalities like Poincaré and log-Sobolev. Covers properties, applications to Lipschitz functions, and various measure settings.
Gaussian Isoperimetry and Related Topics III
Explore Gaussian isoperimetry's applications in probability and analysis, including concentration inequalities, noise stability, and Sobolev-type inequalities. Learn proof methods from geometric measure theory.