Edge universality for non-Hermitian random matrices

G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields (2020).

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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.
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2020-09-25
Journal Title
Probability Theory and Related Fields
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IST-REx-ID

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Cipolloni G, Erdös L, Schröder DJ. Edge universality for non-Hermitian random matrices. Probability Theory and Related Fields. 2020. doi:10.1007/s00440-020-01003-7
Cipolloni, G., Erdös, L., & Schröder, D. J. (2020). Edge universality for non-Hermitian random matrices. Probability Theory and Related Fields. https://doi.org/10.1007/s00440-020-01003-7
Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Edge Universality for Non-Hermitian Random Matrices.” Probability Theory and Related Fields, 2020. https://doi.org/10.1007/s00440-020-01003-7.
G. Cipolloni, L. Erdös, and D. J. Schröder, “Edge universality for non-Hermitian random matrices,” Probability Theory and Related Fields, 2020.
Cipolloni G, Erdös L, Schröder DJ. 2020. Edge universality for non-Hermitian random matrices. Probability Theory and Related Fields.
Cipolloni, Giorgio, et al. “Edge Universality for Non-Hermitian Random Matrices.” Probability Theory and Related Fields, Springer Nature, 2020, doi:10.1007/s00440-020-01003-7.
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