Topic: local-to-global arguments

Localization schemes offer a framework for proving functional inequalities governing Markov chains. This talk introduces the Chen–Eldan approach and shows how local-to-global arguments from high-dimensional expansion fit within it. Examples illustrate the connection and its use in analysing stochastic processes.

Expansion properties of low-dimensional links can propagate through a simplicial complex. This talk presents recent results for partite high-dimensional expanders and their consequences for approximate sampling. It explains how Lorentzian and log-concave polynomials provide the mathematical basis for these local-to-global arguments.