EVENT DETAILS AND ABSTRACT

Title: Trickle-Down in Localization Schemes and Applications
Speaker: Frederic Koehler
Speaker Info: University of Chicago
Brief Description: Trickle-Down in Localization Schemes and Applications
Special Note:
Abstract:

Trickle-down is a phenomenon in high-dimensional expanders with many important applications — for example, it is a key ingredient in various constructions of high-dimensional expanders or the proof of rapid mixing for the basis exchange walk on matroids and in the analysis of log-concave polynomials. I will introduce trickle-down and also discuss recent work, joint with Nima Anari and June Vuong, which was motivated by the idea of generalizing trickle-down beyond high-dimensional expanders. This is guided in part by recent developments in mixing time analysis such as "localization schemes", recently introduced by Yuansi Chen and Ronen Eldan, as well as the related concepts of "entropic stability and independence". In particular, this has led us to an improved mixing time analysis for many models, such as the Sherrington-Kirkpatrick spin glass and its generalization to the O(N) model, as well as the design of a new rapidly mixing Markov chain called the "polarized walk" for a related class of models.