Statistics of infinite dimensional random matrix ensembles

TL;DR

This paper investigates the statistical properties of eigenvalues in large complex non-Hermitian random matrices from the Ginibre ensemble, revealing stable structures and analogies with charge systems in the thermodynamic limit.

Contribution

It introduces the statistical behavior of eigenvalues in infinite-dimensional non-Hermitian matrices and draws analogies with electrical charge systems, expanding understanding of complex Ginibre ensembles.

Findings

Eigenenergies form stable structures in the large matrix limit

Analogies between eigenvalue distributions and charge systems are established

Insights into quantum systems with energy dissipation are provided

Abstract

A quantum statistical system with energy dissipation is studied. Its statisitics is governed by random complex-valued non-Hermitean Hamiltonians belonging to complex Ginibre ensemble. The eigenenergies are shown to form stable structure in thermodynamical limit (large matrix dimension limit). Analogy of Wigner and Dyson with system of electrical charges is drawn.