Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 21 (2016), paper no. 55, 11 pp.
Vector-valued semicircular limits on the free Poisson chaos
In this note, we prove a multidimensional counterpart of the central limit theorem on the free Poisson chaos recently proved by Bourguin and Peccati (2014). A noteworthy property of convergence toward the semicircular distribution on the free Poisson chaos is obtained as part of the limit theorem: component-wise convergence of sequences of vectors of multiple integrals with respect to a free Poisson random measure toward the semicircular distribution implies joint convergence. This result complements similar findings for the Wiener chaos by Peccati and Tudor (2005), the classical Poisson chaos by Peccati and Zheng (2010) and the Wigner chaos by Nourdin, Peccati and Speicher (2013).
Electron. Commun. Probab. Volume 21 (2016), paper no. 55, 11 pp.
Received: 29 March 2016
Accepted: 1 August 2016
First available in Project Euclid: 2 September 2016
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Bourguin, Solesne. Vector-valued semicircular limits on the free Poisson chaos. Electron. Commun. Probab. 21 (2016), paper no. 55, 11 pp. doi:10.1214/16-ECP12. https://projecteuclid.org/euclid.ecp/1472830237