Stochastic Localization with Non-Gaussian Tilts and Applications to Tensor Ising Models
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912237302579200 |
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| author | Mikulincer, Dan Piana, Arianna |
| author_facet | Mikulincer, Dan Piana, Arianna |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_12720 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stochastic Localization with Non-Gaussian Tilts and Applications to Tensor Ising Models Mikulincer, Dan Piana, Arianna Probability Mathematical Physics Functional Analysis 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. |
| title | Stochastic Localization with Non-Gaussian Tilts and Applications to Tensor Ising Models |
| topic | Probability Mathematical Physics Functional Analysis |
| url | https://arxiv.org/abs/2412.12720 |