Sergei M. Gorbunov

collaborators

4 papers

math.PR2026

Gessel-Type Expansion for the Circular $I^^{2}$ -Ensemble and Central Limit Theorem for the Sine- $I^^{2}$ Process for $I^^{2} \leq 2$

Sergei M. Gorbunov

We obtain a Gessel-type expansion in Jack polynomials for the expectations of multiplicative functionals in the circular $I^^{2}$ -ensemble. As a consequence, we establish a SzegÅ-type…

math.FA2026

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

Sergei M. Gorbunov

We consider the convergence of additive functionals under the determinantal point process with the confluent hypergeometric kernel, corresponding to a sufficiently smooth function…

math.FA2026

Unitary transform diagonalizing the Confluent Hypergeometric kernel

Sergei M. Gorbunov

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…

math.FA2025

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

Sergei M. Gorbunov

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 convenie…

Gessel-Type Expansion for the Circular I^2-Ensemble and Central Limit Theorem for the Sine-I^2 Process for I^2≤2

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

Unitary transform diagonalizing the Confluent Hypergeometric kernel

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

Gessel-Type Expansion for the Circular $I^^{2}$ -Ensemble and Central Limit Theorem for the Sine- $I^^{2}$ Process for $I^^{2} \leq 2$