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arXiv · 2505.16069

Central limit theorem for the determinantal point process with the confluent hypergeometric kernel

Sergei M. Gorbunov
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Abstract

We consider the convergence of additive functionals under the determinantal point process with the confluent hypergeometric kernel, corresponding to a sufficiently smooth function $f(x/R)$, as $R\to\infty$. We show that these functionals approach Gaussian distribution and give an estimate on the Kolmogorov-Smirnov distance. To obtain these results, we derive an exact identity for expectations of multiplicative functionals in terms of Fredholm determinants.

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BibTeXRIS

Sergei M. Gorbunov. 2025-05-21. Central limit theorem for the determinantal point process with the confluent hypergeometric kernel. https://arxiv.org/abs/2505.16069

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