Some notes on higher order concentration of measure
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908446706630656 |
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| author | Sambale, Holger |
| author_facet | Sambale, Holger |
| contents | This survey-type paper provides a common framework for a larger number of higher order concentration results (i.\,e., concentration results for non-Lipschitz functions which have bounded derivatives of higher order) in the spirit of Bobkov--Götze--Sambale (2019). Situations inlude measures satisfying various functional inequalities (log-Sobolev, Poincaré, $\mathrm{LS}_q$), uniform and cone measures on spheres with respect to the Euclidean as well as $\ell_p^n$-norms, Stiefel and Grassmann manifolds as well as discrete situations. In particular in the latter case, some open questions and remarks are stated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_08692 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some notes on higher order concentration of measure Sambale, Holger Probability This survey-type paper provides a common framework for a larger number of higher order concentration results (i.\,e., concentration results for non-Lipschitz functions which have bounded derivatives of higher order) in the spirit of Bobkov--Götze--Sambale (2019). Situations inlude measures satisfying various functional inequalities (log-Sobolev, Poincaré, $\mathrm{LS}_q$), uniform and cone measures on spheres with respect to the Euclidean as well as $\ell_p^n$-norms, Stiefel and Grassmann manifolds as well as discrete situations. In particular in the latter case, some open questions and remarks are stated. |
| title | Some notes on higher order concentration of measure |
| topic | Probability |
| url | https://arxiv.org/abs/2507.08692 |