2023/10/23 by Osman, Mohammed
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)
paper · doi:10.48550/arxiv.2310.15001
We consider complex, weakly non-Hermitian matrices A = W1 +i√(τN)W2 , where W1 and W2 are Hermitian matrices and τN = O(N-1). We first show that for pairs of Hermitian matrices (W1 , W2) such that W1 satisfies a multi-resolvent local law and W2 is bounded in norm, the bulk correlation functions of the weakly non-Hermitian Gauss-divisible matrix A + √(t)B converge pointwise to a universal limit for t = O(N-1+ε). Using this and the reverse heat flow we deduce bulk universality in the case when W1 and W2 are independent Wigner matrices with sufficiently smooth density.