Reading seminar on stochastic localization

We devote to study the stochastic localization technique introduced by Ronen Eldan. This beautifal and powerful tool has found broad uses in many difficult problems. The goal of this reading seminar is to understand the idea through several concrete examples, and eventually we go to the general localization scheme framework. There will be three 1-hour lectures scheduled on the following dates/times: April 14, 21, 28th, 3-4pm in Noyes Lab, room 161 . Contact the following email for any questions/comments.

Contact: qiangwu2 [at] illinois [dot] edu

Update: This Friday (May 5th), we will have the last lecture at 3-4pm in Altgeld Hall 145.

References (partial list)

► R. Eldan, Analysis of high-dimensional distributions using pathwise methods, link

► Y. Chen, R. Eldan, Localization Schemes: A Framework for Proving Mixing Bounds for Markov Chains, link

► R. Eldan, F. Koehler, O. Zeitouni, A Spectral Condition for Spectral Gap: Fast Mixing in High-Temperature Ising Models, link

► R. Eldan, D, Mikulincer, P. Raghavendra, Noise stability on the Boolean hypercube via a renormalized Brownian motion, link

► R. Eldan, R, Gross, Concentration on the Boolean hypercube via pathwise stochastic analysisn, link

► Y. Chen, An Almost Constant Lower Bound of the Isoperimetric Coefficient in the KLS Conjecture, link

► A. Alaoui, A. Montanari, M. Sellke, Sampling from the Sherrington-Kirkpatrick Gibbs measure via algorithmic stochastic localization, link

► Y. Chen, R. Eldan, Hit-and-run mixing via localization schemes, link

► A. Alaoui, A. Montanari, An Information-Theoretic View of Stochastic Localization, link

► R.Eldan, Gaussian-width gradient complexity, reverse log-Sobolev inequalities and nonlinear large deviations, link

► R. Eldan, Taming correlations through entropy-efficient measure decompositions with applications to mean-field approximation, link

► R. Eldan, Thin shell implies spectral gap up to polylog via a stochastic localization scheme, link