Stochastic Localization with Non-Gaussian Tilts and Applications to Tensor Ising Models

Abstract

We present generalizations and modifications of Eldan's Stochastic Localization process, extending it to incorporate non-Gaussian tilts, making it useful for a broader class of measures. As an application, we introduce new processes that enable the decomposition and analysis of non-quadratic potentials on the Boolean hypercube, with a specific focus on quartic polynomials. Using this framework, we derive new spectral gap estimates for tensor Ising models under Glauber dynamics, resulting in rapid mixing.

35 pages, 3 figures. New version contains a completely new decomposition theorem into non-negative measures