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SUMMARY:Local semicircle law and level repulsion for Wigner random matrice
 s - Benjamin Schlein (Cambridge)
DTSTART:20090210T140000Z
DTEND:20090210T150000Z
UID:TALK16833@talks.cam.ac.uk
CONTACT:HoD Secretary\, DPMMS
DESCRIPTION:Consider ensembles of N by N hermitian random matrices with in
 dependent and identically distributed entries (up to the symmetry constrai
 nts)\, scaled so that the typical distance between successive eigenvalues 
 is of the order 1/N. In this talk\, I am going to discuss some properties 
 of the spectrum of these matrices as N tends to infinity. In particular\, 
 I am going to present a proof of the validity of the semicircle law for th
 e eigenvalue density on energy scales of the order K/N\, in the limit of l
 arge but fixed K (independent of N). This is the smallest scale on which t
 he semicircle law can be expected to hold. Moreover\, I am going to discus
 s some upper bounds on the probability of finding eigenvalues in a given i
 nterval\, which show the phenomenon of level repulsion. This is a joint wo
 rk with L. Erdos and H.-T. Yau. 
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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