Seminar Announcement
Date: Monday, 7 April 2025
Time: 3:30 PM
Venue: Seminar Hall
Taming quantum randomness with distributional invariance principles
Claus Koestler
UCC - National University of Ireland.
07-04-25

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Abstract

Distributional invariance principles lead to profound structural results in classical probability theory. For example, the de Finetti theorem characterizes an infinite sequence of random variables as conditionally independent and identically distributed if and only if their joint distribution is invariant under permutations of these variables. Recently, there has been significant progress in extending such de Finetti-type results to an operator algebraic framework of quantum probability. In this talk, I will discuss a new distributional invariance principle, called 'partial spreadability'. It connects the Markovianity of a sequence of noncommutative random variables to the representation theory of the Thompson monoid $F^+$, or the Thompson group $F$ in the case of bilateral sequences. Joint work with Stephen Wills and Arundhathi Krishnan.