# Student Probability Seminar

#### Log-Sobolev inequalities for mixture distributions

**Speaker:**
Sinho Chewi, MIT

**Location:**
Online

**Date:**
Wednesday, March 10, 2021, 9 a.m.

**Synopsis:**

Functional inequalities, such as Poincaré inequalities and log-Sobolev inequalities, have played a central role in subjects such as: the concentration of measure phenomenon, mixing of Markov processes, statistical physics, and the geometry of metric measure spaces. I will give a crash course on these inequalities and why they are useful. Then, I will discuss some recent progress on functional inequalities for mixture distributions. If time permits, I will present the recent solution of a conjecture of Bardet. et al. on the log-Sobolev constant of Gaussian convolutions of measures with bounded support (joint work with Hong-Bin Chen and Jonathan Niles-Weed).