Computation of some examples of Brown's spectral measure in free probability
Philippe Biane, Franz Lehner
Abstract
We use free probability techniques for computing spectra and Brown measures of some non hermitian operators in finite von Neumann algebras. Examples include un+uoo where un and uoo are the generators of Zn and Z respectively, in the free product group Zn*Z, or elliptic elements, of the form Sa+iSb where Sa and Sb are free semi-circular elements of variance a and b. We give some pictorial evidence for connections with spectra of random matrices.
Create a lesson
Related papers
Selfless Reduced Crossed Product C*-Algebras Arising from Almost Periodic Actions
Syuichi Ohshima
A Centroid Framework for Operator-Valued Haagerup Inequalities
Patrick Oliveira Santos
Weak Factorization and Product Systems Over Groupoids
Jon Bannon, Alina Vdovina
Representation stability for compact and discrete quantum groups
Michael Brannan, Junichiro Matsuda, Erik Séguin
Warped cones associated to isometric free actions do not have geometric property (T)
Ryo Toyota
Non-Subhomogeneity of Minimal Operator Systems over Positive Semidefinite and Lorentz Cones
Tim Netzer