2023/08/24 by Sergey Berezin, Berezin, Sergey
Economics, Econometrics and Finance · Mathematics · #Complex Systems and Time Series Analysis #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2308.12658
openalex publication_date 2023/08/24 · openalex created_date 2023/08/26 · openalex updated_date 2026/07/28
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).