- Abstract:
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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...
Expand abstract - Publication status:
- Published
- Peer review status:
- Peer reviewed
- Version:
- Accepted Manuscript
- Files:
-
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(pdf, 328.1KB)
-
- Publisher copy:
- 10.1088/1361-6544/aa9d57
-
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- 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:
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1361-6544
- ISSN:
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0951-7715
- Pubs id:
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pubs:657243
- URN:
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uri:9deda560-8319-4dde-9866-d4fb32f39cf9
- UUID:
-
uuid:9deda560-8319-4dde-9866-d4fb32f39cf9
- Local pid:
- pubs:657243
- Copyright holder:
- IOP Publishing Ltd & London Mathematical Society
- Copyright date:
- 2018
- Notes:
-
Copyright © 2018 IOP Publishing Ltd & London Mathematical Society. This is the accepted manuscript version of the article. The final version is available online from IOP Publishing at: https://doi.org/10.1088/1361-6544/aa9d57
Journal article
On the ratio probability of the smallest eigenvalues in the Laguerre unitary ensemble
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