Second order freeness and fluctuations of random matrices. III: Higher order freeness and free cumulants.
Semigroups related to additive and multiplicative, free and Boolean convolutions
Belinschi and Nica introduced a composition semigroup of maps on the set of probability measures. Using this semigroup, they introduced a free divisibility indicator, from which one can know quantitatively if a measure is freely infinitely divisible or not. In the first half of the paper, we further investigate this indicator: we calculate how the indicator changes with respect to free and Boolean powers; we prove that free and Boolean 1/2-stable laws have free divisibility indicators equal to infinity;...
Sharp uniform convexity and smoothness inequalities for trace norms.
Some comments on quantum probability
Some remarks on the convergence in measure and on a dominated sequence of operators measurable with respect to a semifinite von Neumann algebra
Some results on non-commutative Banach function spaces.
Spectral distribution of the free Jacobi process associated with one projection
Given an orthogonal projection P and a free unitary Brownian motion in a W*-non commutative probability space such that Y and P are *-free in Voiculescu’s sense, we study the spectral distribution νₜ of Jₜ = PYₜPYₜ*P in the compressed space. To this end, we focus on the spectral distribution μₜ of the unitary operator SYₜSYₜ*, S = 2P - 1, whose moments are related to those of Jₜ via a binomial-type expansion already obtained by Demni et al. [Indiana Univ. Math. J. 61 (2012)]. In this connection,...
Stable laws and domains of attraction in free probability theory.