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Large Gap Asymptotics for Airy Kernel Determinants with Discontinuities
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
Institut de Recherche en Mathématique et Physique, Université Catholique de Louvain, Chemin du Cyclotron 2, Louvain-la-Neuve, 1348, Belgium.
2019 (English)In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916Article in journal (Refereed) Published
Abstract [en]

We obtain large gap asymptotics for Airy kernel Fredholm determinants with any number m of discontinuities. These m-point determinants are generating functions for the Airy point process and encode probabilistic information about eigenvalues near soft edges in random matrix ensembles. Our main result is that the m-point determinants can be expressed asymptotically as the product of m 1-point determinants, multiplied by an explicit constant pre-factor which can be interpreted in terms of the covariance of the counting function of the process.

Place, publisher, year, edition, pages
Springer New York LLC , 2019.
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Mathematics
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URN: urn:nbn:se:kth:diva-263271DOI: 10.1007/s00220-019-03538-wScopus ID: 2-s2.0-85069823118OAI: oai:DiVA.org:kth-263271DiVA, id: diva2:1368045
Note

QC 20191105

Available from: 2019-11-05 Created: 2019-11-05 Last updated: 2019-11-05Bibliographically approved

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Charlier, Christophe

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