  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).
