Geodesic
Computation of some examples of Brown's spectral measure in free probability
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
Colloquium Mathematicum, Tome 90 (2001) no. 2, pp. 181-211 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

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 
@article{10_4064_cm90_2_3,
     author = {Philippe Biane and Franz Lehner},
     title = {Computation of some examples of {Brown's
spectral} measure in free probability},
     journal = {Colloquium Mathematicum},
     pages = {181--211},
     year = {2001},
     volume = {90},
     number = {2},
     doi = {10.4064/cm90-2-3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/cm90-2-3/}
}
TY  - JOUR
AU  - Philippe Biane
AU  - Franz Lehner
TI  - Computation of some examples of Brown's
spectral measure in free probability
JO  - Colloquium Mathematicum
PY  - 2001
SP  - 181
EP  - 211
VL  - 90
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4064/cm90-2-3/
DO  - 10.4064/cm90-2-3
LA  - en
ID  - 10_4064_cm90_2_3
ER  - 
%0 Journal Article
%A Philippe Biane
%A Franz Lehner
%T Computation of some examples of Brown's
spectral measure in free probability
%J Colloquium Mathematicum
%D 2001
%P 181-211
%V 90
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4064/cm90-2-3/
%R 10.4064/cm90-2-3
%G en
%F 10_4064_cm90_2_3
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

Cité par Sources :