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SUMMARY:Wegner estimate and level repulsion for Wigner random matrices - E
 rdos\, L (Ludwig-Maximilians-Universitt Mnchen)
DTSTART:20081215T163000Z
DTEND:20081215T173000Z
UID:TALK15722@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:We consider N x N Hermitian random matrices with independent i
 dentically distributed entries (Wigner matrices). The matrices are normali
 zed so that the average spacing between consecutive eigenvalues is of orde
 r 1/N. Under suitable assumptions on the distribution of the single matrix
  element\, we first prove that\, away from the spectral edges\, the empiri
 cal density of eigenvalues concentrates around the Wigner semicircle law o
 n energy scales of order 1/N. This result establishes the semicircle law o
 n the optimal scale and it removes a logarithmic factor from our previous 
 result. We then show a Wegner estimate\, i.e. that the averaged density of
  states is bounded. Finally\, we prove that the eigenvalues of a Wigner ma
 trix repel each other\, in agreement with the universality conjecture.
LOCATION:Seminar Room 1\, Newton Institute
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