arXiv subjects

Sergei M. Gorbunov

Publications and source records attributed to Sergei M. Gorbunov.

4 recordsLinked to original sources

arXiv2026

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

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.

math.FA↗

arXiv2026

Gessel-Type Expansion for the Circular $β$-Ensemble and Central Limit Theorem for the Sine-$β$ Process for $β\le 2$

We obtain a Gessel-type expansion in Jack polynomials for the expectations of multiplicative functionals in the circular $β$-ensemble. As a consequence, we establish a Szegő-type limit theorem for all $H^{1/2}(\mathbb{T})$ functions when $β\le 2$, together with an explicit rate of convergence for functions from $H^1(\mathbb{T})$. The estimate is stable under the scaling limit to the sine-$β$ process and yields a Soshnikov-type central limit theorem for the sine-$β$ process in the full $H^{1/2}(\mathbb{R})$ class.

math.PR↗

arXiv2026

Unitary transform diagonalizing the Confluent Hypergeometric kernel

We consider the image of the operator inducing the determinantal point process with the confluent hypergeometric kernel. The space is described as the image of $L_2[0, 1]$ under a unitary transform, which generalizes the Fourier transform. For the derived transform we prove a counterpart of the Paley-Wiener theorem. We use the theorem to prove that the corresponding analogue of the Wiener-Hopf operator is a unitary equivalent of the usual Wiener-Hopf operator, which implies that it shares the same factorization properties and Widom's trace formula. Finally, using the introduced transform we give explicit formulae for the hierarchical decomposition of the image of the operator induced by the confluent hypergeometric kernel.

math.FA↗

arXiv2025

Speed of convergence in the Central Limit Theorem for the determinantal point process with the Bessel kernel

We consider a family of linear operators, diagonalized by the Hankel transform. The Fredholm determinants of these operators, restricted to $L_2[0, R]$, are expressed in a convenient form for asymptotic analysis as $R\to\infty$. The result is an identity, in which the determinant is equal to the leading asymptotic multiplied by an asymptotically small factor, for which an explicit formula is derived. We apply the result to the determinantal point process with the Bessel kernel, calculating the speed of the convergence of additive functionals with respect to the Kolmogorov-Smirnov metric.

math.FA↗