Random Matrices with Merging Singularities and the Painlevé V Equation
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Random Matrices with Merging Singularities and the Painlevé V Equation
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| Creator |
Claeys, T.
Fahs, B. |
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| Description |
We study the asymptotic behavior of the partition function and the correlation kernel in random matrix ensembles of the form 1Zn∣∣det(M²−tI)∣∣αe−nTrV(M)dM, where M is an n×n Hermitian matrix, α>−1/2 and t∈R, in double scaling limits where n→∞ and simultaneously t→0. If t is proportional to 1/n², a transition takes place which can be described in terms of a family of solutions to the Painlevé V equation. These Painlevé solutions are in general transcendental functions, but for certain values of α, they are algebraic, which leads to explicit asymptotics of the partition function and the correlation kernel.
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| Date |
2019-02-15T18:50:36Z
2019-02-15T18:50:36Z 2016 |
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| Type |
Article
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| Identifier |
Random Matrices with Merging Singularities and the Painlevé V Equation / T. Claeys, B. Fahs // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 33 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 60B20; 35Q15; 33E1 DOI:10.3842/SIGMA.2016.031 http://dspace.nbuv.gov.ua/handle/123456789/147729 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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