Asymptotics of the deformed Fredholm determinant of the confluent hypergeometric kernel

Dan Dai; Yu Zhai

doi:10.1111/sapm.12528

Author(s)

Related Research Unit(s)

Department of Mathematics

Detail(s)

Original language	English
Pages (from-to)	1032-1085
Journal / Publication	Studies in Applied Mathematics
Volume	149
Issue number	4
Online published	22 Aug 2022
Publication status	Published - Nov 2022

Link(s)

DOI	DOI https://doi.org/10.1111/sapm.12528 Final Published version
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Attachment(s)	Documents 115478279.pdf Post-print, 2.34 MB, PDF Publisher's Copyright Statement COPYRIGHT TERMS OF DEPOSITED POSTPRINT FILE: This is the peer reviewed version of the following article: Dai, D., & Zhai, Y. (2022). Asymptotics of the deformed Fredholm determinant of the confluent hypergeometric kernel. Studies in Applied Mathematics, 149(4), 1032-1085, which has been published in final form at https://doi.org/10.1111/sapm.12528. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. This article may not be enhanced, enriched or otherwise transformed into a derivative work, without express permission from Wiley or by statutory rights under applicable legislation. Copyright notices must not be removed, obscured or modified. The article must be linked to Wiley’s version of record on Wiley Online Library and any embedding, framing or otherwise making available the article or pages thereof by third parties from platforms, services and websites other than Wiley Online Library must be prohibited.
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Permanent Link	https://scholars.cityu.edu.hk/en/publications/publication(7207a5eb-262b-4d06-bf5f-8245d4968571).html

Abstract

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