Poisson approximations on the free Wigner chaos

DOI10.1214/12-AOP815zbMath1281.46057arXiv1103.3925MaRDI QIDQ359685

Giovanni Peccati, Ivan Nourdin

Publication date: 22 August 2013

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1103.3925

zbMATH Keywords

free Brownian motionfree probabilityCatalan numbersnoncrossing partitionscontractionsfree cumulantssemicircular distributionfree Poisson distributionMarchenko-Pasturnoncentral limit theoremsRiordan numbersWigner chaos

Mathematics Subject Classification ID

Free probability and free operator algebras (46L54) Applications of stochastic analysis (to PDEs, etc.) (60H30) Stochastic integrals (60H05) Stochastic calculus of variations and the Malliavin calculus (60H07)

Related Items (7)

Fisher information and the fourth moment theorem ⋮ Classical and free fourth moment theorems: universality and thresholds ⋮ Freeness characterizations on free chaos spaces ⋮ Poisson convergence on the free Poisson algebra ⋮ Multidimensional limit theorems for homogeneous sums: A survey and a general transfer principle ⋮ Fourth moment theorems for Markov diffusion generators ⋮ Semicircular limits on the free Poisson chaos: counterexamples to a transfer principle

Cites Work

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• Catalan, Motzkin, and Riordan numbers
• Central limit theorems for sequences of multiple stochastic integrals
• Convergence of Wigner integrals to the tetilla law
• Normal Approximations with Malliavin Calculus
• Lectures on the Combinatorics of Free Probability
• Stein's method meets Malliavin calculus: a short survey with new estimates

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