Department of Mathematics - Master Calendar

Title: Transportation Method for Concentration Inequality.

Abstract: Poincaré and log-Sobolev inequalities tell us that the fluctuation of a function of independent random variables is small if the gradient of the function is small and the gradient of a function is a local property. On the other hand, Lipschitz property of function controls this globally. We introduce the characterization of the Lipschitz concentration property on a metric space, called the Bobkov-Götze Theorem. In high dimension, the tensorization principle is useful and we derive this property using the optimal transport theory. Marton's Theorem says that we can get the tensorization of the Lipschitz property thanks to Monge-Kantorovich duality. We will cover these two theorems in this talk.