On tail probability of the covariance matrix in Eldan's stochastic localization
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911113470279680 |
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| author | Guan, Qingyang |
| author_facet | Guan, Qingyang |
| contents | The Eldan's stochastic localization is a new kind of stochastic evolution in the space of probability measures which provides a novel way to study high dimensional convex body. A central object in the study of the stochastic localization is the stochastic process of its covariance matrix. The main result of this paper is some exponential-type tail probability estimate of the covariance process for the general time. This estimate implies a weaker version of a $p$-moment conjecture by Klartag and Lehec. The stochastic localization considered here is a simplified version by Lee and Vemplala. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_14943 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On tail probability of the covariance matrix in Eldan's stochastic localization Guan, Qingyang Probability AMS(2000) Subject Classification: Primary 52A23, Secondary 60H30 The Eldan's stochastic localization is a new kind of stochastic evolution in the space of probability measures which provides a novel way to study high dimensional convex body. A central object in the study of the stochastic localization is the stochastic process of its covariance matrix. The main result of this paper is some exponential-type tail probability estimate of the covariance process for the general time. This estimate implies a weaker version of a $p$-moment conjecture by Klartag and Lehec. The stochastic localization considered here is a simplified version by Lee and Vemplala. |
| title | On tail probability of the covariance matrix in Eldan's stochastic localization |
| topic | Probability AMS(2000) Subject Classification: Primary 52A23, Secondary 60H30 |
| url | https://arxiv.org/abs/2508.14943 |