Edge Universality for non-Hermitian Random Matrices

Abstract

We consider large non-Hermitian real or complex random matrices $X$ with independent, identically distributed centred entries. We prove that their local eigenvalue statistics near the spectral edge, the unit circle, coincide with those of the Ginibre ensemble, i.e. when the matrix elements of $X$ are Gaussian. This result is the non-Hermitian counterpart of the universality of the Tracy-Widom distribution at the spectral edges of the Wigner ensemble.

Updated references, fixed small typos

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Cited by in corpus (9)

• Thermalisation for Wigner matrices
• Optimal Lower Bound on the Least Singular Value of the Shifted Ginibre Ensemble
• On the Spectral Form Factor for Random Matrices
• Infinite stable Boltzmann planar maps are subdiffusive
• Edge Behavior of Higher Complex-Dimensional Determinantal Point Processes
• Quenched universality for deformed Wigner matrices
• The least singular value of the general deformed Ginibre ensemble
• Convergence of the spectral radius of a random matrix through its characteristic polynomial
• Universality of the least singular value for the sum of random matrices