Bulk Universality for Real Matrices with Independent and Identically Distributed Entries

2024/02/06 by Mohammed Osman, Osman, Mohammed · 2 citations
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topics in Algebra #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Matrix Theory and Algorithms #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2402.04071

openalex publication_date 2024/02/06 · openalex created_date 2024/02/08 · openalex updated_date 2026/07/28

Abstract

We consider real, Gauss-divisible matrices A_t=A+√(t)B, where B is from the real Ginibre ensemble. We prove that the bulk correlation functions converge to a universal limit for t=O(N^-1/3+ε) if A satisfies certain local laws. If A=(1)/(√(N))(ξ_jk)_j,k=1^N with ξ_jk independent and identically distributed real random variables having zero mean, unit variance and finite moments, the Gaussian component can be removed using local laws proven by Bourgade--Yau--Yin, Alt--Erdős--Krüger and Cipolloni--Erdős--Schröder and the four moment theorem of Tao--Vu.

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• Characteristic polynomials of non-Hermitian random band matrices
• Bulk Universality for Sparse Complex non-Hermitian Random Matrices

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