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

TL;DR

This paper extends Eldan's Stochastic Localization to non-Gaussian tilts, enabling analysis of non-quadratic potentials and deriving new spectral gap estimates for tensor Ising models, leading to rapid mixing results.

Contribution

It introduces a generalized stochastic localization framework for non-Gaussian measures and applies it to analyze tensor Ising models with quartic potentials.

Findings

New spectral gap estimates for tensor Ising models

Rapid mixing results for Glauber dynamics

Framework for non-quadratic potential analysis

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.