Universality in the random matrix spectra in the regime of weak non-Hermiticity

TL;DR

This paper reviews recent advances in understanding the universal statistical behavior of complex eigenvalues in non-Hermitian random matrices, emphasizing the regime of weak non-Hermiticity and consolidating previous findings.

Contribution

It provides a comprehensive account of the recent progress in characterizing the spectral universality in weakly non-Hermitian random matrices.

Findings

Eigenvalue distributions exhibit universal patterns in the weak non-Hermiticity regime

Connections established between non-Hermitian spectra and Hermitian counterparts

Consolidation of previous results into a unified framework

Abstract

This paper is a detailed account of the recent progress in understanding the statistical properties of complex eigenvalues of random non-Hermitian matrices reported earlier in our two short communications: Physics Letters A v.226, 46 (1997) and Phys. Rev. Lett., v.79, 557 (1997)