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arXiv · 2204.03595

Markovianity and the Thompson Group $F$

Claus Köstler·Arundhathi Krishnan
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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 K\"ummerer, we canonically associate a representation of $F$ to a bilateral stationary Markov process in classical probability.

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Claus Köstler, Arundhathi Krishnan. 2022-04-07. Markovianity and the Thompson Group $F$. https://doi.org/10.3842/sigma.2022.083

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