The top eigenvalue of the random Toeplitz matrix and the sine kernel

• Arnab Sen ^[1] ; Bálint Virág ^[2]
  1. [1] University of Minnesota

     University of Minnesota

     City of Minneapolis, Estados Unidos

     
  2. [2] University of Toronto

     University of Toronto

     Canadá

     
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 41, Nº. 6, 2013, págs. 4050-4079
• Idioma: inglés
• DOI: 10.1214/13-AOP863
• Texto completo no disponible (Saber más ...)
• Resumen

  • We show that the top eigenvalue of an n×n random symmetric Toeplitz matrix, scaled by 2nlogn−−−−−−√, converges to the square of the 2→4 operator norm of the sine kernel.