Characteristic polynomials of complex random matrices and Painlevé transcendents Articles uri icon

publication date

  • May 2020

issue

  • rnaa111

International Standard Serial Number (ISSN)

  • 1073-7928

Electronic International Standard Serial Number (EISSN)

  • 1687-0247

abstract

  • We study expectations of powers and correlation functions for characteristic polynomials of N×N non-Hermitian random matrices. For the 1-point and 2-point correlation function, we obtain several characterizations in terms of Painlevé transcendents, both at finite N and asymptotically as N→∞. In the asymptotic analysis, two regimes of interest are distinguished: boundary asymptotics where parameters of the correlation function can touch the boundary of the limiting eigenvalue support and bulk asymptotics where they are strictly inside the support...