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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2308.12658 |
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| _version_ | 1866914024589885440 |
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| author | Berezin, Sergey |
| author_facet | Berezin, Sergey |
| contents | We consider the hard-edge scaling of the Mittag-Leffler ensemble confined to a fixed disk inside the droplet. Our primary emphasis is on fluctuations of rotationally-invariant additive statistics that depend on the radius and thus give rise to radius-dependent stochastic processes. For the statistics originating from bounded measurable functions, we establish a central limit theorem in the appropriate functional space. By assuming further regularity, we are able to extend the result to a vector functional central limit theorem that additionally includes the first hitting "time" of the radius-dependent statistic. The proof of the first theorem involves an approximation by exponential random variables alongside a coupling technique. The proof of the second result rests heavily on Skorohod's almost sure representation theorem and builds upon a result of Galen Shorack (1973). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_12658 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Functional Central Limit Theorems for Constrained Mittag-Leffler Ensemble in Hard Edge Scaling Berezin, Sergey Probability We consider the hard-edge scaling of the Mittag-Leffler ensemble confined to a fixed disk inside the droplet. Our primary emphasis is on fluctuations of rotationally-invariant additive statistics that depend on the radius and thus give rise to radius-dependent stochastic processes. For the statistics originating from bounded measurable functions, we establish a central limit theorem in the appropriate functional space. By assuming further regularity, we are able to extend the result to a vector functional central limit theorem that additionally includes the first hitting "time" of the radius-dependent statistic. The proof of the first theorem involves an approximation by exponential random variables alongside a coupling technique. The proof of the second result rests heavily on Skorohod's almost sure representation theorem and builds upon a result of Galen Shorack (1973). |
| title | Functional Central Limit Theorems for Constrained Mittag-Leffler Ensemble in Hard Edge Scaling |
| topic | Probability |
| url | https://arxiv.org/abs/2308.12658 |