Limiting eigenvalue distribution of the general deformed Ginibre ensemble

2024/09/03 by Sarapin, Roman
#60B20 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2409.02314

Abstract

Consider the n× n matrix X_n=A_n+H_n, where A_n is a n× n matrix (either deterministic or random) and H_n is a n× n matrix independent from A_n drawn from complex Ginibre ensemble. We study the limiting eigenvalue distribution of X_n. In arXiv:0807.4898 it was shown that the eigenvalue distribution of X_n converges to some deterministic measure. This measure is known for the case A_n=0. Under some general convergence conditions on A_n we prove a formula for the density of the limiting measure. We also obtain an estimation on the rate of convergence of the distribution. The approach used here is based on supersymmetric integration.

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