Poisson convergence on the free Poisson algebra

DOI10.3150/14-BEJ638zbMath1375.46047arXiv1312.2610OpenAlexW1925318460MaRDI QIDQ888477

Solesne Bourguin

Publication date: 30 October 2015

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.2610

zbMATH Keywords

free probabilitycontractionsfourth moment theoremfree Poisson distributionmultiplication formulachaos structurecombinatorics of free Poisson random measuresdiagram formulae

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Free probability and free operator algebras (46L54)

Related Items (2)

Freeness characterizations on free chaos spaces ⋮ Multidimensional limit theorems for homogeneous sums: A survey and a general transfer principle

Cites Work

• Poisson approximations on the free Wigner chaos
• Wigner chaos and the fourth moment
• Noncentral convergence of multiple integrals
• Stein's method on Wiener chaos
• Wiener chaos: Moments, cumulants and diagrams. A survey with computer implementation
• Catalan, Motzkin, and Riordan numbers
• Semicircular limits on the free Poisson chaos: counterexamples to a transfer principle
• Invariance principles for homogeneous sums of free random variables
• Central limit theorems for sequences of multiple stochastic integrals
• Gamma limits and U-statistics on the Poisson space
• Normal Approximations with Malliavin Calculus
• Lectures on the Combinatorics of Free Probability

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