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Markovianity and the Thompson Group $F$
Symmetry, integrability and geometry: methods and applications, Tome 18 (2022) Cet article a éte moissonné depuis la source Math-Net.Ru

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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 Kümmerer, we canonically associate a representation of $F$ to a bilateral stationary Markov process in classical probability.
Keywords: noncommutative stationary Markov processes, representations of Thompson group $F$. 
@article{SIGMA_2022_18_a82,
     author = {Claus K\"ostler and Arundhathi Krishnan},
     title = {Markovianity and the {Thompson} {Group} $F$},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2022},
     volume = {18},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2022_18_a82/}
}
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Claus Köstler; Arundhathi Krishnan. Markovianity and the Thompson Group $F$. Symmetry, integrability and geometry: methods and applications, Tome 18 (2022). http://geodesic.mathdoc.fr/item/SIGMA_2022_18_a82/

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