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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2503.13361 |
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| _version_ | 1866929762288533504 |
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| author | Gamboa, Fabrice Venker, Martin |
| author_facet | Gamboa, Fabrice Venker, Martin |
| contents | We study vectors chosen at random from a compact convex polytope in $\mathbb{R}^n$ given by a finite number of linear constraints. We determine which projections of these random vectors are asymptotically normal as $n\to\infty$. Marginal distributions are also studied, showing that in the large $n$ limit random variables under linear constraints become i.i.d. exponential under a rescaling. Our novel approach is based on a complex de Finetti theorem revealing an underlying independence structure as well as on entropy arguments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_13361 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Limit Theorems Under Several Linear Constraints Gamboa, Fabrice Venker, Martin Probability We study vectors chosen at random from a compact convex polytope in $\mathbb{R}^n$ given by a finite number of linear constraints. We determine which projections of these random vectors are asymptotically normal as $n\to\infty$. Marginal distributions are also studied, showing that in the large $n$ limit random variables under linear constraints become i.i.d. exponential under a rescaling. Our novel approach is based on a complex de Finetti theorem revealing an underlying independence structure as well as on entropy arguments. |
| title | Limit Theorems Under Several Linear Constraints |
| topic | Probability |
| url | https://arxiv.org/abs/2503.13361 |