Peer-Reviewed Journal Details
Mandatory Fields
Köstler, Claus; Krishnan, Arundhathi; Wills, Stephen J
2023
Unknown
Journal of Functional Analysis
Markovianity and the Thompson monoid F+
Published
()
Optional Fields
Distributional invariance principles; Noncommutative De Finetti theorems; Noncommutative stationary Markov processes; Representations of Thompson monoid F+.
284
6
1
70
We introduce a new distributional invariance principle, called ‘partial spreadability’, which emerges from the representation theory of the Thompson monoid 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 . 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.
1096-0783
10.1016/j.jfa.2022.109818
Grant Details
Irish Research Council
Government of Ireland Postdoctoral Fellowship Programme (Project ID: GOIPD/2018/498)