Asymptotics of Orthogonal Polynomial Ensembles via Integrable Methods

Explore the intricacies of orthogonal polynomial ensembles and their asymptotic behavior through integrable methods in this 47-minute lecture by Ken McLAUGHLIN from Colorado State University. Delve into applications of random matrix theory, statistical properties of random variables, and the concept of equilibrium measure. Examine random tilings and their overwhelming probability, as well as discrete orthogonal polynomials. Gain insights into Hilbert analysis, equilibrium measures, and key results in the field. Discover interesting future directions for research in this comprehensive overview of asymptotics in orthogonal polynomial ensembles, presented as part of the School and Workshop on Random Matrix Theory and Point Processes at ICTP Mathematics.

Introduction
Applications
Random variables
Statistical properties
Equilibrium measure
Random tilings
Overwhelming probability
Random tiling
Discrete orthogonal polynomials
Summary
Discrete case
Hilbert analysis
Equilibrium measures
Results
Interesting directions