Large Deviations for Traces of Wigner Matrices

Explore a comprehensive lecture on large deviations for traces of Wigner matrices, presented by Fanny AUGERI from the Weizmann Institute in Rehovot, Israel. Delve into the intricacies of random matrix theory, covering topics such as typical and large deviation behaviors, large deviation principles, and Wigner matrices with bounded entries. Examine examples of lower bounds, speed of large deviations, and universality in large deviations. Investigate the mechanism of large deviations, including lower bounds and special families of changes of measure. Discover nonlinear large deviations, functions of low complexity, and their applications to traces of Wigner matrices. This 44-minute talk, part of the School and Workshop on Random Matrix Theory and Point Processes, offers a deep dive into advanced mathematical concepts for researchers and enthusiasts in the field.

Intro
Typical and large deviations behaviors
Large deviation principles
Wigner matrices with bounded entries
Example of a lower bound
Speed of large deviations
Large deviation result
Wigner matrices with sharp sub-Gaussian tails
Universality in large deviations
Mechanism of large deviations
Large deviation lower bound
A special family of changes of measure
Nonlinear large deviations
Functions of low complexity
Large deviation of traces of Wigner matrices