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The generating function for the Bessel point process and a system of coupled Painleve V equations
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2019 (English)In: Random Matrices. Theory and Applications, ISSN 2010-3263, Vol. 8, no 3, article id 1950008Article in journal (Refereed) Published
Abstract [en]

We study the joint probability generating function for k occupancy numbers on disjoint intervals in the Bessel point process. This generating function can be expressed as a Fredholm determinant. We obtain an expression for it in terms of a system of coupled Painleve V equations, which are derived from a Lax pair of a Riemann-Hilbert problem. This generalizes a result of Tracy and Widom [C. A. Tracy and H. Widom, Level spacing distributions and the Bessel kernel, Commun. Math. Phys. 161(2) (1994) 289-309], which corresponds to the case k = 1. We also provide some examples and applications. In particular, several relevant quantities can be expressed in terms of the generating function, like the gap probability on a union of disjoint bounded intervals, the gap between the two smallest particles, and large n asymptotics for nxn Hankel determinants with a Laguerre weight possessing several jump discontinuities near the hard edge.

Place, publisher, year, edition, pages
World Scientific Publishing Co. Pte Ltd , 2019. Vol. 8, no 3, article id 1950008
Keywords [en]
Riemann-Hilbert problems, Bessel point process, Painleve V equations, Fredholm determinants
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-255759DOI: 10.1142/S2010326319500084ISI: 000477677200001Scopus ID: 2-s2.0-85054083925OAI: oai:DiVA.org:kth-255759DiVA, id: diva2:1342017
Note

QC 20190812

Available from: 2019-08-12 Created: 2019-08-12 Last updated: 2019-08-12Bibliographically approved

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