Multi-variable subordination distributions for free additive convolution
Abstract
Description
Let k be a positive integer and let D_k denote the space of joint distributions for k-tuples of selfadjoint elements in C*-probability space. The paper studies the concept of "subordination distribution of μ\boxplus νwith respect to ν" for μ, ν\in D_k, where \boxplus is the operation of free additive convolution on D_k. The main tools used in this study are combinatorial properties of R-transforms for joint distributions and a related operator model, with operators acting on the full Fock space
Multi-variable subordination turns out to have nice relations to a process of evolution towards \boxplus-infinite divisibility on D_k that was recently found by Belinschi and Nica (arXiv:0711.3787). Most notably, one gets better insight into a connection which this process was known to have with free Brownian motion.
Minor modifications and reference added to 1st version. 34 pages, no figures
Minor modifications and reference added to 1st version. 34 pages, no figures