Quenched universality for deformed Wigner matrices
Cipolloni G, Erdös L, Schröder DJ. 2022. Quenched universality for deformed Wigner matrices. Probability Theory and Related Fields.
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Abstract
Following E. Wigner’s original vision, we prove that sampling the eigenvalue gaps within the bulk spectrum of a fixed (deformed) Wigner matrix H yields the celebrated Wigner-Dyson-Mehta universal statistics with high probability. Similarly, we prove universality for a monoparametric family of deformed Wigner matrices H+xA with a deterministic Hermitian matrix A and a fixed Wigner matrix H, just using the randomness of a single scalar real random variable x. Both results constitute quenched versions of bulk universality that has so far only been proven in annealed sense with respect to the probability space of the matrix ensemble.
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2022-07-23
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Probability Theory and Related Fields
Acknowledgement
The authors are indebted to Sourav Chatterjee for forwarding the very inspiring question that Stephen Shenker originally addressed to him which initiated the current paper. They are also grateful that the authors of [23] kindly shared their preliminary numerical results in June 2021.
Open access funding provided by Institute of Science and Technology (IST Austria).
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Cipolloni G, Erdös L, Schröder DJ. Quenched universality for deformed Wigner matrices. Probability Theory and Related Fields. 2022. doi:10.1007/s00440-022-01156-7
Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). Quenched universality for deformed Wigner matrices. Probability Theory and Related Fields. Springer Nature. https://doi.org/10.1007/s00440-022-01156-7
Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Quenched Universality for Deformed Wigner Matrices.” Probability Theory and Related Fields. Springer Nature, 2022. https://doi.org/10.1007/s00440-022-01156-7.
G. Cipolloni, L. Erdös, and D. J. Schröder, “Quenched universality for deformed Wigner matrices,” Probability Theory and Related Fields. Springer Nature, 2022.
Cipolloni G, Erdös L, Schröder DJ. 2022. Quenched universality for deformed Wigner matrices. Probability Theory and Related Fields.
Cipolloni, Giorgio, et al. “Quenched Universality for Deformed Wigner Matrices.” Probability Theory and Related Fields, Springer Nature, 2022, doi:10.1007/s00440-022-01156-7.
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