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CATEGORIES:Probability
SUMMARY:Local semicircle law and level repulsion for Wigne
r random matrices - Benjamin Schlein (Cambridge)
DTSTART;TZID=Europe/London:20090210T140000
DTEND;TZID=Europe/London:20090210T150000
UID:TALK16833AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/16833
DESCRIPTION:Consider ensembles of N by N hermitian random matr
ices with independent and identically distributed
entries (up to the symmetry constraints)\, scaled
so that the typical distance between successive ei
genvalues 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 parti
cular\, I am going to present a proof of the valid
ity of the semicircle law for the eigenvalue densi
ty on energy scales of the order K/N\, in the limi
t of large but fixed K (independent of N). This is
the smallest scale on which the semicircle law ca
n be expected to hold. Moreover\, I am going to di
scuss some upper bounds on the probability of find
ing eigenvalues in a given interval\, which show t
he phenomenon of level repulsion. This is a joint
work with L. Erdos and H.-T. Yau.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
B
CONTACT:HoD Secretary\, DPMMS
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