Free Brownian motion and evolution towards boxplus-infinite divisibility for k-tuples
Abstract
Let D be the space of non-commutative distributions of k-tuples of selfadjoints in a C*-probability space (for a fixed k). We introduce a semigroup of transformations B_t of D, such that every distribution in D evolves under the B_t towards infinite divisibility with respect to free additive convolution. The very good properties of B_t come from some special connections that we put into evidence between free additive convolution and the operation of Boolean convolution. On the other hand we put into evidence a relation between the transformations B_t and free Brownian motion. More precisely, we introduce a transformation Phi of D which converts the free Brownian motion started at an arbitrary distribution m in D into the process B_t (Phi(m)), t>0.
Keywords
Cite
@article{arxiv.0711.3787,
title = {Free Brownian motion and evolution towards boxplus-infinite divisibility for k-tuples},
author = {Serban T. Belinschi and Alexandru Nica},
journal= {arXiv preprint arXiv:0711.3787},
year = {2007}
}