### Abstract:

Suppose that the global eigenvalue distribution of two large random matrices A and B are known. It is a remarkable fact that, generically, the eigenvalue distribution of A + B and (if A and B are positive definite) A*B are uniquely determined from only the eigenvalue distributions of A and B; i.e., no information about eigenvectors are required. These operations on eigenvalue distributions are described by free probability theory. We construct a numerical toolbox which can efficiently and reliably calculate these operations with spectral accuracy, by exploiting the complex analytical framework that underlies free probability theory.

Speaker

Sheehan Olver

Research Area

Joint Colloquium

Affiliation

University of Sydney

Date

Fri, 20/04/2012 - 2:00pm to 3:00pm

Venue

RC-4082, Red Centre Building, UNSW