Gap Probability for the Hard Edge Pearcey Process

Dan Dai; Shuai-Xia Xu; Lun Zhang

doi:10.1007/s00023-023-01266-5

Gap Probability for the Hard Edge Pearcey Process

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

6 Scopus Citations

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Author(s)

Dan Dai
Shuai-Xia Xu
Lun Zhang

Related Research Unit(s)

Department of Mathematics

Detail(s)

Original language	English
Pages (from-to)	2067–2136
Journal / Publication	Annales Henri Poincare
Volume	24
Issue number	6
Online published	19 Jan 2023
Publication status	Published - Jun 2023

Link(s)

DOI	DOI https://doi.org/10.1007/s00023-023-01266-5 Final Published version
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Attachment(s)	Documents 133774116.pdf Post-print, 663 KB, PDF Publisher's Copyright Statement COPYRIGHT TERMS OF DEPOSITED POSTPRINT FILE: This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s00023-023-01266-5.
Link to Scopus	https://www.scopus.com/record/display.uri?eid=2-s2.0-85146606170&origin=recordpage
Permanent Link	https://scholars.cityu.edu.hk/en/publications/publication(c36d0c21-a938-4fc7-8aa9-c4804e752d52).html

Abstract

The hard edge Pearcey process is universal in random matrix theory and many other stochastic models. This paper deals with the gap probability for the thinned/unthinned hard edge Pearcey process over the interval (0, s) by working on a 3×3 matrix-valued Riemann–Hilbert problem for the relevant Fredholm determinants. We establish an integral representation of the gap probability via the Hamiltonian related to a new system of coupled differential equations. Together with some remarkable differential identities for the Hamiltonian, we derive the large gap asymptotics for the thinned hard edge Pearcey process, including the explicitly evaluation of the constant factor in terms of the Barnes G-function. As an application, we also obtain the asymptotic statistical properties of the counting function for the hard edge Pearcey process.

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