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Weak and Strong Confinement in the Freud Random Matrix Ensemble and Gap Probabilities

Claeys, t.
•
Krasovsky, I.
•
Minakov, O.
2023
  • journal article

Periodico
COMMUNICATIONS IN MATHEMATICAL PHYSICS
Abstract
The Freud ensemble of random matrices is the unitary invariant ensemble corresponding to the weight exp(-n vertical bar x vertical bar(beta)), beta > 0, on the real line. We consider the local behaviour of eigenvalues near zero, which exhibits a transition in beta. If beta >= 1, it is described by the standard sine process. Below the critical value beta = 1, it is described by a process depending on the value of beta, and we determine the first two terms of the large gap probability in it. This so called weak confinement range 0 < beta < 1 corresponds to the Freud weight with the indeterminate moment problem. We also find the multiplicative constant in the asymptotic expansion of the Freud multiple integral for beta >= 1.
DOI
10.1007/s00220-023-04749-y
WOS
WOS:001008615200001
Archivio
https://hdl.handle.net/20.500.11767/135530
info:eu-repo/semantics/altIdentifier/scopus/2-s2.0-85163138006
https://arxiv.org/abs/2209.07253
https://ricerca.unityfvg.it/handle/20.500.11767/135530
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