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 matrices

Add to your list(s) Download to your calendar using vCal

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.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.

 

© 2006-2019 Talks.cam, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity