Towards the bulk universality of non-Hermitian random matrices
Abstract
We consider the non-Hermitian analogue of the celebrated Wigner-Dyson-Mehta bulk universality phenomenon, i.e. that in the bulk the local eigenvalue statistics of a large random matrix with independent, identically distributed centred entries are universal, in particular they asymptotically coincide with those of the Ginibre ensemble in the corresponding symmetry class. In this paper we reduce this problem to understanding a certain microscopic regime for the Hermitized resolvent in Girko's formula by showing that all other regimes are negligible.
Keywords
Cite
@article{arxiv.1909.06350,
title = {Towards the bulk universality of non-Hermitian random matrices},
author = {Giorgio Cipolloni and László Erdős and Dominik Schröder},
journal= {arXiv preprint arXiv:1909.06350},
year = {2020}
}
Comments
We have reformulated the main result from the previous version, so that now it reduces the bulk universality to a question about singular value universality of shifted iid matrices. arXiv admin note: text overlap with arXiv:1908.00969