Random Matrices with Merging Singularities and the Painlevé V Equation
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,...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2016 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2016
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/147729 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | 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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| ISSN: | 1815-0659 |