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Eigenvalues of truncated unitary matrices : disk counting statistics

Ameur, Yacin LU ; Charlier, Christophe LU and Moreillon, Philippe (2023) In Monatshefte fur Mathematik
Abstract

Let T be an n× n truncation of an (n+ α) × (n+ α) Haar distributed unitary matrix. We consider the disk counting statistics of the eigenvalues of T. We prove that as n→ + ∞ with α fixed, the associated moment generating function enjoys asymptotics of the form exp(C1n+C2+o(1)), where the constants C1 and C2 are given in terms of the incomplete Gamma function. Our proof uses the uniform asymptotics of the incomplete Beta function.

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author
; and
organization
publishing date
type
Contribution to journal
publication status
in press
subject
keywords
Disk counting statistics, Moment generating functions, Random matrix theory
in
Monatshefte fur Mathematik
publisher
Springer
external identifiers
  • scopus:85176737118
ISSN
0026-9255
DOI
10.1007/s00605-023-01920-4
language
English
LU publication?
yes
id
7cf3dcb6-7866-4bc5-adc0-e8f6a6e95d5a
date added to LUP
2024-01-04 15:26:19
date last changed
2024-01-04 15:27:11
@article{7cf3dcb6-7866-4bc5-adc0-e8f6a6e95d5a,
  abstract     = {{<p>Let T be an n× n truncation of an (n+ α) × (n+ α) Haar distributed unitary matrix. We consider the disk counting statistics of the eigenvalues of T. We prove that as n→ + ∞ with α fixed, the associated moment generating function enjoys asymptotics of the form exp(C1n+C2+o(1)), where the constants C<sub>1</sub> and C<sub>2</sub> are given in terms of the incomplete Gamma function. Our proof uses the uniform asymptotics of the incomplete Beta function.</p>}},
  author       = {{Ameur, Yacin and Charlier, Christophe and Moreillon, Philippe}},
  issn         = {{0026-9255}},
  keywords     = {{Disk counting statistics; Moment generating functions; Random matrix theory}},
  language     = {{eng}},
  publisher    = {{Springer}},
  series       = {{Monatshefte fur Mathematik}},
  title        = {{Eigenvalues of truncated unitary matrices : disk counting statistics}},
  url          = {{http://dx.doi.org/10.1007/s00605-023-01920-4}},
  doi          = {{10.1007/s00605-023-01920-4}},
  year         = {{2023}},
}