Pseudo-hermitian random matrix theory: a review

Abstract We review our recent results on pseudo-hermitian random matrix theory which were hitherto presented in various conferences and talks. (Detailed accounts of work will appear soon separate publications.) Following an introduction this new type matrices, we focus two specific models matrices are with respect to a given indefinite metric B. Eigenvalues either real, or come complex-conjugate pairs. The diagrammatic method is applied deriving explicit analytical expressions for the density eigenvalues complex plane real axis, large- N , planar limit. In one discuss, B depends certain parameter t. As t varies, model exhibits ‘phase transitions’ associated flowing from onto causing disjoint eigenvalue support intervals merge. Our agree well numerical simulations.