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

Dan Mikulincer; Arianna Piana

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arXiv · 2412.12720

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

Dan Mikulincer·Arianna Piana

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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.

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BibTeX RIS

Dan Mikulincer, Arianna Piana. 2024-12-17. Stochastic Localization with Non-Gaussian Tilts and Applications to Tensor Ising Models. https://arxiv.org/abs/2412.12720

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