# Probability and Mathematical Physics Seminar

## Confinement of Unimodal Probability Distributions and an FKG-Gaussian Correlation Inequality

### Time and Location:

April 26, 2024 at 11:10AM; Warren Weaver Hall, Room 1302## Speaker:

Mark Sellke, Harvard University## Link:

Seminar homepage## Abstract:

While unimodal probability distributions are well understood in dimension 1, the same cannot be said in high dimension without imposing stronger conditions such as log-concavity. I will explain a new approach to proving confinement (e.g. variance upper bounds) for high-dimensional unimodal distributions which are not log-concave, based on an extension of Royen’s celebrated Gaussian correlation inequality. We will see how it yields new localization results for Ginzburg-Landau random surfaces with very general monotone potentials. Time permitting, I will also discuss a related result on the effective mass of the Fröhlich Polaron, which is joint work with Rodrigo Bazaes, Chiranjib Mukherjee, and S.R.S. Varadhan.