Arundhathi Krishnan (UCC)

will speak on

Markovianity and the Thompson monoid F+

Time: 4:20PM
Date: Tue 26th November 2019
Location: Seminar Room SCN 1.25 [map]

Abstract: In the process of identifying a suitable distributional symmetry to describe Markovianity, it has been conjectured by C. K\'ostler that there is a certain correspondence between unilateral Markov shifts and representations of the Thompson monoid $F^+$. After having illustrated this correspondence in the context of tensor products of $W^*$-algebraic probability spaces, I will present the following two general results. A representation of the Thompson monoid $F^+$ in the endomorphisms of a $W^*$-algebraic probability space yields a noncommutative Markov process (in the sense of K\'ummerer). Conversely, such a representation is obtained from a noncommutative Markov process which is given as coupling to a so-called spreadable noncommutative Bernoulli shift.

(This talk is part of the Analysis series.)

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