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arXiv · 2310.11429

Bulk Universality for Complex non-Hermitian Matrices with Independent and Identically Distributed Entries

Anna Maltsev·Mohammed Osman
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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.

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Anna Maltsev, Mohammed Osman. 2023-10-17. Bulk Universality for Complex non-Hermitian Matrices with Independent and Identically Distributed Entries. https://doi.org/10.1007/s00440-024-01321-0

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