Seminars & Colloquia Calendar

Abstract: For a probability measure $\mu$ on the discrete hypercube, we are interested in finding sufficient conditions under which $\mu$ either (a) Exhibits concentration (either in the sense of Lipschitz functions, or in a stronger sense such as a Poincare inequality), or (b) Can be expressed as a mixture of a rather small number of "localized" measures which in turn exhibit some sort of concentration. We will present several results in those directions, whose proofs all rely on a localization technique that we will try to explain. We will mention some applications of these results towards mean field approximation, pure state decomposition, mixing time of the Glauber dynamics on Ising models and concentration of negatively dependent variables. Based on joint works with Koehler, Shamir and Zeitouni.