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arXiv · 2606.18162

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

Vitonofrio Crismale·Yun Gang Lu·Éric Ricard
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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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Vitonofrio Crismale, Yun Gang Lu, Éric Ricard. 2026-06-16. Periodicity, type $II_1$ factors and free Poisson laws in interacting Fock spaces. https://arxiv.org/abs/2606.18162

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