Localization and delocalization for heavy tailed band matrices
Florent Benaych-Georges, Sandrine Péché (2014)
Annales de l'I.H.P. Probabilités et statistiques
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We consider some random band matrices with band-width whose entries are independent random variables with distribution tail in . We consider the largest eigenvalues and the associated eigenvectors and prove the following phase transition. On the one hand, when , the largest eigenvalues have order , are asymptotically distributed as a Poisson process and their associated eigenvectors are essentially carried by two coordinates (this phenomenon has already been remarked for full matrices...