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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2309.01263 |
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| _version_ | 1866913259447123968 |
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| author | Polaczyk, Bartłomiej |
| author_facet | Polaczyk, Bartłomiej |
| contents | We answer an open problem posed by Mossel--Oleszkiewicz--Sen regarding relations between $p$-log-Sobolev inequalities for $p\in(0,1]$. We show that for any interval $I\subset(0,1]$, there exist $q,p\in I$, $q<p$, and a measure $μ$ for which the $q$-log-Sobolev inequality holds, while the $p$-log-Sobolev inequality is violated. As a tool we develop certain necessary and closely related sufficient conditions characterizing those inequalities in the case of birth-death processes on $\mathbb{N}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_01263 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | $P$-log-Sobolev inequalities on $\mathbb{N}$ Polaczyk, Bartłomiej Probability 60E15 We answer an open problem posed by Mossel--Oleszkiewicz--Sen regarding relations between $p$-log-Sobolev inequalities for $p\in(0,1]$. We show that for any interval $I\subset(0,1]$, there exist $q,p\in I$, $q<p$, and a measure $μ$ for which the $q$-log-Sobolev inequality holds, while the $p$-log-Sobolev inequality is violated. As a tool we develop certain necessary and closely related sufficient conditions characterizing those inequalities in the case of birth-death processes on $\mathbb{N}$. |
| title | $P$-log-Sobolev inequalities on $\mathbb{N}$ |
| topic | Probability 60E15 |
| url | https://arxiv.org/abs/2309.01263 |