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 limit.

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