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University of Cambridge > Talks.cam > Probability > Local semicircle law and level repulsion for Wigner random matrices

## Local semicircle law and level repulsion for Wigner random matricesAdd to your list(s) Download to your calendar using vCal - Benjamin Schlein (Cambridge)
- Tuesday 10 February 2009, 14:00-15:00
- MR12, CMS, Wilberforce Road, Cambridge, CB3 0WB.
If you have a question about this talk, please contact HoD Secretary, DPMMS. Consider ensembles of N by N hermitian random matrices with independent and identically distributed entries (up to the symmetry constraints), 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 the eigenvalue density on energy scales of the order K/N, in the limit of large but fixed K (independent of N). This is the smallest scale on which the semicircle law can be expected to hold. Moreover, I am going to discuss some upper bounds on the probability of finding eigenvalues in a given interval, which show the phenomenon of level repulsion. This is a joint work with L. Erdos and H.-T. Yau. This talk is part of the Probability series. ## This talk is included in these lists:- All CMS events
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