Skip to content

Computation of some examples of Brown's spectral measure in free probability

Philippe Biane, Franz Lehner

math.OAarXiv:math/9912242

Abstract

We use free probability techniques for computing spectra and Brown measures of some non hermitian operators in finite von Neumann algebras. Examples include un+uoo where un and uoo are the generators of Zn and Z respectively, in the free product group Zn*Z, or elliptic elements, of the form Sa+iSb where Sa and Sb are free semi-circular elements of variance a and b. We give some pictorial evidence for connections with spectra of random matrices.

Create a lesson