4 papers
Lecture Notes on "Free Probability Theory"
Roland Speicher
This in an introduction to free probability theory, covering the basic combinatorial and analytic theory, as well as the relations to random matrices and operator algebras. The mat…
Entrywise application of non-linear functions on orthogonally invariant matrices
Roland Speicher, Alexander Wendel
In this article, we investigate how the entrywise application of a non-linear function to symmetric orthogonally invariant random matrix ensembles alters the spectral distribution.…
Computing the noncommutative inner rank by means of operator-valued free probability theory
Johannes Hoffmann, Tobias Mai, Roland Speicher
We address the noncommutative version of the Edmonds' problem, which asks to determine the inner rank of a matrix in noncommuting variables. We provide an algorithm for the calcula…
Fuglede-Kadison determinants of matrix-valued semicircular elements and capacity estimates
Tobias Mai, Roland Speicher
We calculate the Fuglede-Kadison determinant of arbitrary matrix-valued semicircular operators in terms of the capacity of the corresponding covariance mapping. We also improve a l…