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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.

Keywords

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