The slicing conjecture via small ball estimates
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866909454597881856 |
|---|---|
| author | Bizeul, Pierre |
| author_facet | Bizeul, Pierre |
| contents | Bourgain's slicing conjecture was recently resolved by Joseph Lehec and Bo'az Klartag. We present an alternative proof by establishing small ball probability estimates for isotropic log-concave measures. Our approach relies on the stochastic localization process and Guan's bound, techniques also used by Klartag and Lehec. The link between small ball probabilities and the slicing conjecture was first observed by Dafnis and Paouris and is established through Milman's theory of M-ellipsoids. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_06854 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The slicing conjecture via small ball estimates Bizeul, Pierre Functional Analysis Probability Bourgain's slicing conjecture was recently resolved by Joseph Lehec and Bo'az Klartag. We present an alternative proof by establishing small ball probability estimates for isotropic log-concave measures. Our approach relies on the stochastic localization process and Guan's bound, techniques also used by Klartag and Lehec. The link between small ball probabilities and the slicing conjecture was first observed by Dafnis and Paouris and is established through Milman's theory of M-ellipsoids. |
| title | The slicing conjecture via small ball estimates |
| topic | Functional Analysis Probability |
| url | https://arxiv.org/abs/2501.06854 |