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

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