Eigenvalues of truncated unitary matrices : disk counting statistics
(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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https://lup.lub.lu.se/record/7cf3dcb6-7866-4bc5-adc0-e8f6a6e95d5a
- author
- Ameur, Yacin LU ; Charlier, Christophe LU and Moreillon, Philippe
- organization
- publishing date
- 2023
- 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}}, }