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Authors: Vitonofrio Crismale ×

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arXiv (math.PR) 2026-06-17 DOI: arXiv:2606.18162

Periodicity, type $II_1$ factors and free Poisson laws in interacting Fock spaces

Authors:

Vitonofrio Crismale ↗Yun Gang Lu ↗\'Eric Ricard ↗

arXiv:2606.18162v1 Announce Type: cross Abstract: We show that the von Neumann algebra generated by position operators in a 2-periodic interacting Fock space is a type $II_1$ 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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