Geodesic
Computation of some examples of Brown's spectral measure in free probability
Philippe Biane1 ; Franz Lehner2
1 CNRS DMA 45 rue d'Ulm 75005 Paris, France
2 Institut für Analysis und Numerik Johannes Kepler Universität Linz 4040 Linz, Austria and Équipe d'Analyse Université Paris 6 Boîte 186, Tour 46-0 4, place Jussieu 75252 Paris Cedex 05, France
Colloquium Mathematicum, Tome 90 (2001) no. 2, pp. 181-211.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We use free probability techniques to compute spectra and Brown measures of some non-hermitian operators in finite von Neumann algebras. Examples include $u_n+u_{\infty }$ where $u_n$ and $u_{\infty }$ are the generators of ${\mathbb Z}_n$ and ${\mathbb Z}$ respectively, in the free product ${\mathbb Z}_n\mathbin {*}{\mathbb Z}$, or elliptic elements of the form $S_{\alpha }+iS_{\beta }$ where $S_\alpha $ and $S_\beta $ are free semicircular elements of variance $\alpha $ and $\beta $.
DOI : 10.4064/cm90-2-3
Keywords: probability techniques compute spectra brown measures non hermitian operators finite von neumann algebras examples include infty where infty generators mathbb mathbb respectively product mathbb mathbin * mathbb elliptic elements form alpha beta where alpha beta semicircular elements variance alpha beta

Philippe Biane 1 ; Franz Lehner 2

1 CNRS DMA 45 rue d'Ulm 75005 Paris, France
2 Institut für Analysis und Numerik Johannes Kepler Universität Linz 4040 Linz, Austria and Équipe d'Analyse Université Paris 6 Boîte 186, Tour 46-0 4, place Jussieu 75252 Paris Cedex 05, France 
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Philippe Biane; Franz Lehner. Computation of some examples of Brown's
spectral measure in free probability. Colloquium Mathematicum, Tome 90 (2001) no. 2, pp. 181-211. doi : 10.4064/cm90-2-3. http://geodesic.mathdoc.fr/articles/10.4064/cm90-2-3/

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