Markovianity and the Thompson Monoid $F^+$
Operator Algebras
2022-12-22 v4 Group Theory
Probability
Abstract
We introduce a new distributional invariance principle, called `partial spreadability', which emerges from the representation theory of the Thompson monoid in noncommutative probability spaces. We show that a partially spreadable sequence of noncommutative random variables is adapted to a local Markov filtration. Conversely we show that a large class of noncommutative stationary Markov sequences provides representations of the Thompson monoid . In the particular case of a classical probability space, we arrive at a de Finetti theorem for stationary Markov sequences with values in a standard Borel space.
Keywords
Cite
@article{arxiv.2009.14811,
title = {Markovianity and the Thompson Monoid $F^+$},
author = {Claus Köstler and Arundhathi Krishnan and Stephen J. Wills},
journal= {arXiv preprint arXiv:2009.14811},
year = {2022}
}
Comments
Revised introduction, some minor additions and corrections. 61 pages. To appear in J. Funct. Anal