|Speaker:||Joshua Feinberg (University of Haifa)|
|Title:||Pseudo-hermitian Random Matrix Theory: Theory & Practice|
|Date (JST):||Tue, Jun 28, 2022, 13:30 - 14:30|
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
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