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