Stability of Klartag's improved Lichnerowicz inequality
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911845199118336 |
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| author | Courtade, Thomas A. Fathi, Max |
| author_facet | Courtade, Thomas A. Fathi, Max |
| contents | In a recent work, Klartag gave an improved version of Lichnerowicz' spectral gap bound for uniformly log-concave measures, which improves on the classical estimate by taking into account the covariance matrix. We analyze the equality cases in Klartag's bound, showing that it can be further improved whenever the measure has no Gaussian factor. Additionally, we give a quantitative improvement for log-concave measures with finite Fisher information. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_12277 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability of Klartag's improved Lichnerowicz inequality Courtade, Thomas A. Fathi, Max Functional Analysis Metric Geometry Probability In a recent work, Klartag gave an improved version of Lichnerowicz' spectral gap bound for uniformly log-concave measures, which improves on the classical estimate by taking into account the covariance matrix. We analyze the equality cases in Klartag's bound, showing that it can be further improved whenever the measure has no Gaussian factor. Additionally, we give a quantitative improvement for log-concave measures with finite Fisher information. |
| title | Stability of Klartag's improved Lichnerowicz inequality |
| topic | Functional Analysis Metric Geometry Probability |
| url | https://arxiv.org/abs/2404.12277 |