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

Philippe Biane, and Franz Lehner. "Computation of some examples of Brown's spectral measure in free probability." Colloquium Mathematicae 90.2 (2001): 181-211. <http://eudml.org/doc/283888>.

@article{PhilippeBiane2001,
abstract = {We use free probability techniques to compute spectra and Brown measures of some non-hermitian operators in finite von Neumann algebras. Examples include $uₙ + u_\{∞\}$ where uₙ and $u_\{∞\}$ are the generators of ℤₙ and ℤ respectively, in the free product ℤₙ*ℤ, or elliptic elements of the form $S_\{α\} + iS_\{β\}$ where $S_\{α\}$ and $S_\{β\}$ are free semicircular elements of variance α and β.},
author = {Philippe Biane, Franz Lehner},
journal = {Colloquium Mathematicae},
keywords = {free convolutions; spectral measure; free probability theory; Brown measure; von Neumann algebras},
language = {eng},
number = {2},
pages = {181-211},
title = {Computation of some examples of Brown's spectral measure in free probability},
url = {http://eudml.org/doc/283888},
volume = {90},
year = {2001},
}

TY - JOUR
AU - Philippe Biane
AU - Franz Lehner
TI - Computation of some examples of Brown's spectral measure in free probability
JO - Colloquium Mathematicae
PY - 2001
VL - 90
IS - 2
SP - 181
EP - 211
AB - We use free probability techniques to compute spectra and Brown measures of some non-hermitian operators in finite von Neumann algebras. Examples include $uₙ + u_{∞}$ where uₙ and $u_{∞}$ are the generators of ℤₙ and ℤ respectively, in the free product ℤₙ*ℤ, or elliptic elements of the form $S_{α} + iS_{β}$ where $S_{α}$ and $S_{β}$ are free semicircular elements of variance α and β.
LA - eng
KW - free convolutions; spectral measure; free probability theory; Brown measure; von Neumann algebras
UR - http://eudml.org/doc/283888
ER -