Asymptotics of the deformed Fredholm determinant of the confluent hypergeometric kernel

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Original languageEnglish
Pages (from-to)1032-1085
Journal / PublicationStudies in Applied Mathematics
Issue number4
Online published22 Aug 2022
Publication statusPublished - Nov 2022


In this paper, we consider the deformed Fredholm determinant of the confluent hypergeometric kernel. This determinant represents the gap probability of the corresponding determinantal point process where each particle is removed independently with probability 1- γ, 0 ≤ γ < 1. We derive asymptotics of the deformed Fredholm determinant when the gap interval tends to infinity, up to and including the constant term. As an application of our results, we establish a central limit theorem for the eigenvalue counting function and a global rigidity upper bound for its maximum deviation.

Research Area(s)

  • confluent hypergeometric kernel, Fredholm determinant, gap probability, PAINLEVE-II, UNIVERSALITY, TOEPLITZ, AIRY, DISTRIBUTIONS, SOLVABILITY, POLYNOMIALS, ENSEMBLES, HANKEL, BESSEL