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. As the main application, I will deduce localization for random surface models 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.

Speaker:

Mark Sellke is an Assistant Professor of Statistics at Harvard. He received his PhD in mathematics from Stanford, where he was advised by Andrea Montanari and Sebastien Bubeck. His research interests are a mix of probability and machine learning.