Confinement of Unimodal Probability Distributions and an FKGGaussian Correlation Inequality
Confinement of Unimodal Probability Distributions and an FKGGaussian Correlation Inequality

Mark Sellke, Harvard University
Fine Hall 224
While unimodal probability distributions are well understood in dimension 1, the same cannot be said in high dimension without imposing stronger conditions such as logconcavity. I will explain a new approach to proving confinement (e.g. variance upper bounds) for highdimensional unimodal distributions which are not logconcave, 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 with Rodrigo Bazaes, Chiranjib Mukherjee, and S.R.S. Varadhan.