University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Wegner estimate and level repulsion for Wigner random matrices

Wegner estimate 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 Mustapha Amrani.

Mathematics and Physics of Anderson localization: 50 Years After

We consider N x N Hermitian random matrices with independent identically distributed entries (Wigner matrices). The matrices are normalized so that the average spacing between consecutive eigenvalues is of order 1/N. Under suitable assumptions on the distribution of the single matrix element, we first prove that, away from the spectral edges, the empirical density of eigenvalues concentrates around the Wigner semicircle law on energy scales of order 1/N. This result establishes the semicircle law on 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 matrix repel each other, in agreement with the universality conjecture.

This talk is part of the Isaac Newton Institute Seminar Series 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