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Research Papers

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

S. M. Gorbunov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

Abstract: For a determinantal point process with confluent hypergeometric kernel, the convergence of additive functionals is studied. The functionals correspond to a sufficiently smooth function $f(x/R)$, as $R\to\infty$. It is shown that these functionals approach the Gaussian distribution, and an estimate on the Kolmogorov–Smirnov distance is given. To obtain these results, an exact identity is derived for expectations of multiplicative functionals in terms of Fredholm determinants.

Keywords: regularized additive functional, limit theorems, Fredholm determinants, expectation.

Received: 20.05.2025

Language: English