Mathematical Physics Seminar

Singular values and inter-relations between classical random matrix ensembles

Peter Forrester, Professor, Department of Mathematics, University of Melbourne,

In the case of random matrix ensembles with an orthogonal symmetry, superimposing

two spectra drawn at random gives a simple function form for the

eigenvalue PDF. This functional form naturally separates the even labelled, and the odd labelled,

eigenvalues. For particular Laguerre and Jacobi weights, integrating over the odd labelled

eigenvalues gives back the PDF for a random matrix ensemble with unitary symmetry. After revising known

results of this type, and their consequences for gap probabilities, analogous findings in

relation to singular values will be presented.

Event Sponsors:

For more information, please contact Eric Rains by email at [email protected].