• Corpus ID: 235485278

Quenched universality for deformed Wigner matrices

  title={Quenched universality for deformed Wigner matrices},
  author={Giorgio Cipolloni and L'aszl'o ErdHos and Dominik Schroder},
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 matrixA and a fixed Wigner matrixH , just using the randomness of a single scalar real random variable x. Both results constitute quenched… 
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