2024-09-272024-09-272023-03-13Koestler, C., Krishnan, A. and Wills, S. (2023) 'Markovianity and the Thompson monoid F+', Journal of Functional Analysis, 284(6), available: https://doi.org/10.1016/j.jfa.2022.109818.0022-1236https://dspace.mic.ul.ie/handle/10395/3333We 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.eng24 Months CC BY-NC-NDhttps://www.sciencedirect.com/science/article/pii/S0022123622004384Distributional Invariance PrinciplesNoncommutative De Finetti TheoremsNoncommutative Stationary Markov ProcessesRepresentations of Thompson monoid F+Article10.1016/j.jfa.2022.109818