Bulk Universality for Complex non-Hermitian Matrices with Independent and Identically Distributed Entries
Probability
2024-09-30 v5 Mathematical Physics
math.MP
Abstract
We consider N x N matrices with complex entries that are perturbed by a complex Gaussian matrix with small variance. We prove that if the unperturbed matrix satisfies certain local laws then the bulk correlation functions are universal in the large N limit. Assuming the entries are independent and identically distributed with a common distribution that has finite moments, the Gaussian component is removed by the four moment theorem of Tao and Vu.
Cite
@article{arxiv.2310.11429,
title = {Bulk Universality for Complex non-Hermitian Matrices with Independent and Identically Distributed Entries},
author = {Anna Maltsev and Mohammed Osman},
journal= {arXiv preprint arXiv:2310.11429},
year = {2024}
}
Comments
Revised version