Stochastic Localization with Non-Gaussian Tilts and Applications to Tensor Ising Models
Probability
2025-02-20 v2 Mathematical Physics
Functional Analysis
math.MP
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.
Cite
@article{arxiv.2412.12720,
title = {Stochastic Localization with Non-Gaussian Tilts and Applications to Tensor Ising Models},
author = {Dan Mikulincer and Arianna Piana},
journal= {arXiv preprint arXiv:2412.12720},
year = {2025}
}
Comments
35 pages, 3 figures. New version contains a completely new decomposition theorem into non-negative measures