Free probability in Physics

Question

Recently I have started reading some materials on non-commutative probability. IN this area mathematicians sometimes consider quantum theory as a non-commutative version of classical probability, with some extra conditions. With this starting point axiomatic version of quantum field theory has also been tried to construct. Based on tensor product types, bosonic and fermionic systems come up naturally. I want to know about the third type of noncommutative probability, i.e. free probability. This has been introduced by Voiculescu to attack the free group factor isomorphism problems. Is there any physical significance of free probability? Does there exists any connections between free probability and some physical systems (like symmetric and antisymmetric tensor product had with bosonic and fermionic systems).

Advanced thanks for any reply. Also please provide some references (paper or books), which describes such connection(s), if exists,

This post imported from StackExchange Physics at 2015-09-02 17:39 (UTC), posted by SE-user RSG

Comments

In case you haven't seen it, Terence Tao's notes on free probability seem a good introduction: terrytao.wordpress.com/2010/02/10/245a-notes-5-free-probability. The following link is about free probability and quantum information theory, not physical processes, but it may be of interest: perimeterinstitute.ca/videos/….

This post imported from StackExchange Physics at 2015-09-02 17:39 (UTC), posted by SE-user Ernie