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

Philippe Biane·Franz Lehner
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Abstract

We use free probability techniques for computing spectra and Brown measures of some non hermitian operators in finite von Neumann algebras. Examples include u_n+u_oo where u_n and u_oo are the generators of Z_n and Z respectively, in the free product group Z_n*Z, or elliptic elements, of the form S_a+iS_b where S_a and S_b 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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Philippe Biane, Franz Lehner. 1999-12-31. Computation of some examples of Brown's spectral measure in free probability. https://arxiv.org/abs/math/9912242

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