Asymptotics of the deformed Fredholm determinant of the confluent hypergeometric kernel

Dan Dai; Yu Zhai

doi:10.1111/sapm.12528

Asymptotics of the deformed Fredholm determinant of the confluent hypergeometric kernel

Dan Dai^*, Yu Zhai

^*Corresponding author for this work

Department of Mathematics

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

6 Citations (Scopus)

55 Downloads (CityUHK Scholars)

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.

Original language	English
Pages (from-to)	1032-1085
Journal	Studies in Applied Mathematics
Volume	149
Issue number	4
Online published	22 Aug 2022
DOIs	https://doi.org/10.1111/sapm.12528
Publication status	Published - Nov 2022

Funding

Dan Dai was partially supported by grants from the City University of Hong Kong (Project No. 7005252 and 7005597), and a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CityU 11300520).

Research Keywords

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

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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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.",

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Asymptotics of the deformed Fredholm determinant of the confluent hypergeometric kernel

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GRF: Spacing Problems in Random Matrix Theory

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Asymptotics of the deformed Fredholm determinant of the confluent hypergeometric kernel

Abstract

Funding

Research Keywords

Publisher's Copyright Statement

RGC Funding Information

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GRF: Spacing Problems in Random Matrix Theory

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