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 …

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 …