Multidimensional semicircular limits on the free Wigner chaos

Details Multidimensional semicircular limits on the free Wigner chaos Multidimensional semicircular limits on the free Wigner chaos

2011-07-26

arxiv.org/abs/1107.5135v1

Mathematics

Probability

11 pages

Scientific paper

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).

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