Speaker: Joshua Feinberg (University of Haifa)
Title: Pseudo-hermitian Random Matrix Theory: Theory & Practice
Date (JST): Tue, Jun 28, 2022, 13:30 - 14:30
Place: ISSP
Abstract: Pseudo-hermitian random matrices form a new class of matrix models
lying between the classical Wigner-Dyson ensembles of hermitian
matrices and the non-hermitian Ginibre ensembles. These matrices are
hermitian with respect to an indefinite metric over some vector space.
Consequently, their eigenvalues are either real or come in complex
conjugate pairs.
Ensembles of pseudo-hermitian random matrices could be thought of
probability measures over generators of the non-compact classical Lie
algebras, in complete analogy to classical hermitian random matrices
being probability measures over the classical compact algebras.
In this talk I will explain the physical motivation for
pseudo-hermitian random matrix theory and present explicit numerical
and analytical results pertaining to the average eigenvalue spectrum
of a concrete pseudo-hermitian random matrix model in the large-N