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math.OA2013★ 8 cited
Poisson convergence on the free Poisson algebra
Solesne Bourguin
Based on recent findings by Bourguin and Peccati, we give a fourth moment type condition for an element of a free Poisson chaos of arbitrary order to converge to a free (centered)…
math.OA2013
Semicircular limits on the free Poisson chaos: counterexamples to a transfer principle
Solesne Bourguin, Giovanni Peccati
We establish a class of sufficient conditions, ensuring that a sequence of multiple integrals with respect to a free Poisson measure converges to a semicircular limit. We use this…