Periodicity, type II1 factors and free Poisson laws in interacting Fock spaces
Abstract
We show that the von Neumann algebra generated by position operators in a 2-periodic interacting Fock space is a type II1 factor. On the probabilistic side, we prove that the squared position operators have a Marchenko-Pastur distribution with respect to the vacuum state, yielding a natural realization of free Poisson laws within this framework.
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