Transport inequalities for random point measures
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866917698948038656 |
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| author | Gozlan, Nathael Herry, Ronan Peccati, Giovanni |
| author_facet | Gozlan, Nathael Herry, Ronan Peccati, Giovanni |
| contents | We derive transport-entropy inequalities for mixed binomial point processes, and for Poisson point processes. We show that when the finite intensity measure satisfies a Talagrand transport inequality, the law of the point process also satisfies a Talagrand type transport inequality. We also show that a Poisson point process (with arbitrary $σ$-finite intensity measure) always satisfies a universal transport-entropy inequality à la Marton. We explore the consequences of these inequalities in terms of concentration of measure and modified logarithmic Sobolev inequalities. In particular, our results allow one to extend a deviation inequality by Reitzner [31], originally proved for Poisson random measures with finite mass. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2002_04923 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Transport inequalities for random point measures Gozlan, Nathael Herry, Ronan Peccati, Giovanni Probability Functional Analysis 60G55, 60E15, 46E27 We derive transport-entropy inequalities for mixed binomial point processes, and for Poisson point processes. We show that when the finite intensity measure satisfies a Talagrand transport inequality, the law of the point process also satisfies a Talagrand type transport inequality. We also show that a Poisson point process (with arbitrary $σ$-finite intensity measure) always satisfies a universal transport-entropy inequality à la Marton. We explore the consequences of these inequalities in terms of concentration of measure and modified logarithmic Sobolev inequalities. In particular, our results allow one to extend a deviation inequality by Reitzner [31], originally proved for Poisson random measures with finite mass. |
| title | Transport inequalities for random point measures |
| topic | Probability Functional Analysis 60G55, 60E15, 46E27 |
| url | https://arxiv.org/abs/2002.04923 |