Functional Central Limit Theorems for Constrained Mittag-Leffler Ensemble in Hard Edge Scaling
arXiv:2308.12658 · doi:10.1214/25-EJP1400
Abstract
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).
arXiv comment27 pages. Accepted version
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