Lozenge Tilings via the Dynamic Loop Equation
Explore discrete Markov chains with particle interactions, focusing on lozenge tilings and their asymptotic behavior using holomorphic observables.
Adaptive Robustness and Sub-Gaussian Deviations in Sparse Linear Regression - Probability and Statistics Seminar
Explore robust estimation in sparse linear models with corrupted observations and heavy-tailed noise. Learn adaptive procedures for optimal signal estimation and sub-Gaussian deviations.
Anticoncentration in Ramsey Graphs and Proof of the Erdös-McKay Conjecture - Lecture
Explore Ramsey graphs and the proof of the Erdös-McKay Conjecture, focusing on edge-statistics and anticoncentration in these unique graph structures.
Integral Varadhan Formula for Nonlinear Heat Flow on Measured Finsler Manifolds
Explore integral Varadhan formula for nonlinear heat flow on measured Finsler manifolds, examining particle probability and distance relationships in geometric analysis.
Probability Distribution Formulas
Explore formulas for binomial, geometric, Poisson, uniform, and exponential probability distributions. Master key concepts to solve statistical problems effectively.
Kurdyka-Łojasiewicz Exponent for Hadamard-Difference-Parameterized Models
Explore Kurdyka-Łojasiewicz exponents in L1-regularized optimization, focusing on Hadamard difference parametrization and its impact on local convergence rates of gradient methods.
Counting Limit Theorems for Representations of Gromov-Hyperbolic Groups
Explore limit theorems for Gromov-hyperbolic group representations, examining statistical results analogous to random matrix products theory for spherical averages in the S-metric.
A Non-symmetric Kesten Criterion for Random Walks on Groups
Explore a non-symmetric version of Kesten's criterion for random walks on countable groups, relating to amenability and probability of return to identity.
Around the Joint Behavior of Independent Random Tensor Matrices - Lecture 3
Explore advanced topics in free probability theory, focusing on joint behavior of independent random tensor matrices and symmetry groups, with applications in matrix analysis.
Around the Joint Behavior of Independent Random Tensor Matrices - Lecture 2
Explore advanced topics in free probability theory, focusing on joint behavior of independent random tensor matrices and symmetry groups, with applications in matrix analysis.
Functional Relations for Higher Order Free Cumulants and Moments
Explore functional relations between generating series of cumulants and moments in higher order free probability. Gain insights into matrix models and topological recursion.
Around the Joint Behavior of Independent Random Tensor Matrices - Lecture 1
Explore joint behavior of independent random tensor matrices with smaller symmetry groups. Learn about tensor structures, generalizations of free probability, and new analytical techniques.
Singularity of Stationary Measures in Markov Chains
Explore stationary measures of compound Markov chains, focusing on examples using boundary processes of random walks on the modular group PSL(2,Z) and related classical constructions.
Constrained Stochastic Processes: From Brownian Motion to Run-and-Tumble Particles
Explore constrained stochastic processes, including Brownian motion, Lévy flights, and run-and-tumble particles. Learn effective dynamics for generating constrained trajectories in various scenarios.
Harmonic Maps and Random Walks on Countable Groups
Explore harmonic maps and random walks on countable groups, focusing on CAT(0) spaces and group actions with zero escape rate.
The Simplest Proof of Cayley's Formula and Its Connection to Statistical Mechanics
Explore Cayley's Formula's simplest proof and its statistical mechanics connection in this insightful lecture by Alexei Rebenko from the National Academy of Sciences, Kiev.
Fractional Response and Parameter Almost Sure Invariance Principle for the Quadratic Family
Explore statistical properties of quadratic family dynamics, including almost sure invariance principle and its implications for ergodic averages and fractional response.
Dynamical Subsets in Iterated Function Systems
Explore dynamical subsets in iterated function systems with Henna Koivusalo's in-depth analysis of rare events in dynamical systems.
Rare Events Point Processes in Infinite Measure Dynamical Systems
Explore rare events point processes in infinite measure dynamical systems, focusing on hitting and return time statistics and their applications to Manneville-Pommeau maps.
Generalized Law of Iterated Logarithm in the Infinite Horizon Lorentz Gas
Explore the behavior of infinite horizon Lorentz gas, focusing on chaotic dynamics, long flights, and non-standard scaling in limit theorems for billiard particle positions.
Quantitative Recurrence for Z-Extension of Three-Dimensional Axiom A Flows
Explore quantitative recurrence in Z-extension of Axiom A flows, focusing on first return time behavior and applications to geodesic flows on Z-cover of compact surfaces.