The Poisson transport map
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
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| _version_ | 1866915140722491392 |
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| author | López-Rivera, Pablo Shenfeld, Yair |
| author_facet | López-Rivera, Pablo Shenfeld, Yair |
| contents | We construct a transport map from Poisson point processes onto ultra-log-concave measures over the natural numbers, and show that this map is a contraction. Our approach overcomes the known obstacles to transferring functional inequalities using transport maps in discrete settings, and allows us to deduce a number of functional inequalities for ultra-log-concave measures. In particular, we provide the currently best known constant in modified logarithmic Sobolev inequalities for ultra-log-concave measures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_02359 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Poisson transport map López-Rivera, Pablo Shenfeld, Yair Probability 39B62, 60G55, 60H07 We construct a transport map from Poisson point processes onto ultra-log-concave measures over the natural numbers, and show that this map is a contraction. Our approach overcomes the known obstacles to transferring functional inequalities using transport maps in discrete settings, and allows us to deduce a number of functional inequalities for ultra-log-concave measures. In particular, we provide the currently best known constant in modified logarithmic Sobolev inequalities for ultra-log-concave measures. |
| title | The Poisson transport map |
| topic | Probability 39B62, 60G55, 60H07 |
| url | https://arxiv.org/abs/2407.02359 |