PIRSA:10070017

Singular values, complex eigenvalues and the single ring theorem

APA

Zeitouni, O. (2010). Singular values, complex eigenvalues and the single ring theorem. Perimeter Institute. https://pirsa.org/10070017

MLA

Zeitouni, Ofer. Singular values, complex eigenvalues and the single ring theorem. Perimeter Institute, Jul. 05, 2010, https://pirsa.org/10070017

BibTex

          @misc{ pirsa_10070017,
            doi = {},
            url = {https://pirsa.org/10070017},
            author = {Zeitouni, Ofer},
            keywords = {},
            language = {en},
            title = {Singular values, complex eigenvalues and the single ring theorem},
            publisher = {Perimeter Institute},
            year = {2010},
            month = {jul},
            note = {PIRSA:10070017 see, \url{https://pirsa.org}}
          }
          

Abstract

Limit laws and large deviations for the empirical measure of the singular values for ensembles of non-Hermitian matrices can be obtained based on explicit distributions for the eigenvalues. When considering the eigenvalues, however, the situation changes dramatically, and explicit expressions for the joint distribution of eigenvalues are not available (except in very special cases). Nevertheless, in some situations the limit of the empirical measure of eigenvalues (as a measure supported in the complex plane) can be computed, and it exhibits interesting features. I will describe some results along these line, part of a joint work with Alice Guionnet and Manjunath Krishnapur.