Random Matrices with Merging Singularities and the Painlevé V Equation

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2016
• Main Authors: Claeys, T., Fahs, B.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2016
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/147729
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: 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.

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,...