Markovianity and the Thompson Monoid F⁺

2020/09/30 by Köstler, Claus, Krishnan, Arundhathi, Wills, Stephen J. · 1 citation
#FOS: Mathematics #Group Theory (math.GR) #Operator Algebras (math.OA) #Probability (math.PR)

paper · doi:10.48550/arxiv.2009.14811

Abstract

We introduce a new distributional invariance principle, called `partial spreadability', which emerges from the representation theory of the Thompson monoid F⁺ 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 F⁺. 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.

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