2011/07/26 by Ivan Nourdin, Nourdin, Ivan, Giovanni Peccati +3 · 1 citation
Mathematics · #FOS: Mathematics #Operator Algebras (math.OA) #Probability (math.PR) #math.OA #math.PR
paper · pdf · doi:10.48550/arxiv.1107.5135
11 pages
arxiv created 2011/07/26 · arxiv updated 2011/07/27
We show that, for sequences of vectors of multiple Wigner integrals with respect to a free Brownian motion, componentwise convergence to semicircular is equivalent to joint convergence. This result extends to the free probability setting some findings by Peccati and Tudor (2005), and represents a multidimensional counterpart of a limit theorem inside the free Wigner chaos established by Kemp, Nourdin, Peccati and Speicher (2011).