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On the ratio probability of the smallest eigenvalues in the Laguerre unitary ensemble

Abstract:

We study the probability distribution of the ratio between the second smallest and smallest eigenvalue in the n × n Laguerre unitary ensemble. The probability that this ratio is greater than r > 1 is expressed in terms of an n × n Hankel determinant with a perturbed Laguerre weight. The limiting probability distribution for the ratio as n → ∞ is found as an integral over (0, ∞) containing two functions q1(x) and q2(x). These functions satisfy a system of two coupled Painlevé V equations, w...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted Manuscript

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Publisher copy:
10.1088/1361-6544/aa9d57

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Engineering Science
Role:
Author
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Funding agency for:
Zohren, S
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Funding agency for:
Zohren, S
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Funding agency for:
Zohren, S
Publisher:
IOP Publishing Publisher's website
Journal:
Nonlinearity Journal website
Volume:
31
Issue:
4
Pages:
1155-1196
Publication date:
2018-02-19
Acceptance date:
2017-11-27
DOI:
EISSN:
1361-6544
ISSN:
0951-7715
Pubs id:
pubs:657243
URN:
uri:9deda560-8319-4dde-9866-d4fb32f39cf9
UUID:
uuid:9deda560-8319-4dde-9866-d4fb32f39cf9
Local pid:
pubs:657243

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