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arXiv · 2009.14811

Markovianity and the Thompson Monoid $F^+$

Claus Köstler·Arundhathi Krishnan·Stephen J. Wills
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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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Claus Köstler, Arundhathi Krishnan, Stephen J. Wills. 2020-09-30. Markovianity and the Thompson Monoid $F^+$. https://arxiv.org/abs/2009.14811

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