Free Brownian motion and evolution towards boxplus-infinite divisibility for k-tuples

Details Free Brownian motion and evolution towards boxplus-infinite divisibility for k-tuples Free Brownian motion and evolution towards boxplus-infinite divisibility for k-tuples

2007-11-23

arxiv.org/abs/0711.3787v1

Mathematics

Operator Algebras

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Free Brownian motion and evolution towards boxplus-infinite divisibility for k-tuples does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Free Brownian motion and evolution towards boxplus-infinite divisibility for k-tuples, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Free Brownian motion and evolution towards boxplus-infinite divisibility for k-tuples will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-562693