Confinement of unimodal probability distributions and an FKG-Gaussian correlation inequality

Mon May 20th 2024, 4:00pm
Sequoia 200
Mark Sellke, Harvard

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 mention 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.