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DTSTAMP:20260509T134949Z
DESCRIPTION:Title: Quantum unique ergodicity for generalized Wigner matrice
 s.\n\nAbstract: We prove a strong form of delocalization of eigenvectors f
 or general large random matrices called Quantum Unique Ergodicity. This pr
 operty was first given as a conjecture by Rudnick and Sarnak on the eigenf
 unctions of the Laplacian on negatively curved compact Riemannian manifold
 s. In the context of random matrix theory\, these estimates state that the
  mass of an eigenvector over a subset of entries tends to the uniform dist
 ribution with very high probability. We are also able to prove that the fl
 uctuations around the uniform distribution are Gaussian for a regime of su
 bsets of entries. The proof relies on new eigenvector observables studied 
 dynamically through the Dyson Brownian motion combined with a novel bootst
 rap comparison argument. If time allows\, after describing the sketch of t
 he dynamical method in random matrix theory\, we will develop one of these
  arguments.\n\n \n
DTSTART:20220915T153000Z
DTEND:20220915T163000Z
LOCATION:Room 1214
SUMMARY:Lucas Benigni (UdeM)
URL:https://www.mcgill.ca/mathstat/channels/event/lucas-benigni-udem-341762
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