Markovianity and the Thompson Group $F$

Abstract

We show that representations of the Thompson group $F$ in the automorphisms of a noncommutative probability space yield a large class of bilateral stationary noncommutative Markov processes. As a partial converse, bilateral stationary Markov processes in tensor dilation form yield representations of $F$. As an application, and building on a result of Kümmerer, we canonically associate a representation of $F$ to a bilateral stationary Markov process in classical probability.

arXiv admin note: text overlap with arXiv:2009.14811

References in corpus (2)

• Noncommutative independence from the braid group $B_{\infty }$
• On spectral measures for certain unitary representations of R. Thompson's group F