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math.OA2026
Periodicity, type factors and free Poisson laws in interacting Fock spaces
Vitonofrio Crismale, Yun Gang Lu, Ãric Ricard
We show that the von Neumann algebra generated by position operators in a 2-periodic interacting Fock space is a type factor. On the probabilistic side, we prove that the sq…
math.OA2026
Non-commutative Law of iterated logarithm
Sourav Panja, Ãric Ricard, Diptesh Saha
We prove optimal non-commutative analogues of the classical Law of Iterated Logarithm (LIL) for both martingales and sequences of independent (non-commutative) random variables. Th…
math.OA2024
Failure of almost uniformly convergence for noncommutative martingales
Guixiang Hong, Ãric Ricard
In this paper, we provide a counterexample to show that in sharp contrast to the classical case, the almost uniform convergence may not happen for truly noncommutative -martin…