Bulk universality for deformed Wigner matrices

• Lee, Ji Oon ^[2] ; Schnelli, Kevin ^[3] ; Stetler, Ben ^[1] ; Yau, Horng-Tzer ^[1]
  1. [1] Harvard University

     Harvard University

     City of Cambridge, Estados Unidos

     
  2. [2] KAIST
  3. [3] IST Austria

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• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 44, Nº. 3, 2016, págs. 2349-2425
• Idioma: inglés
• DOI: 10.1214/15-AOP1023
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• Resumen

  • We consider N×N random matrices of the form H=W+V where W is a real symmetric or complex Hermitian Wigner matrix and V is a random or deterministic, real, diagonal matrix whose entries are independent of W. We assume subexponential decay for the matrix entries of W, and we choose V so that the eigenvalues of W and V are typically of the same order. For a large class of diagonal matrices V, we show that the local statistics in the bulk of the spectrum are universal in the limit of large N.