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arXiv · 1107.5135

Multidimensional semicircular limits on the free Wigner chaos

Ivan Nourdin·Giovanni Peccati·Roland Speicher
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Abstract

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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Ivan Nourdin, Giovanni Peccati, Roland Speicher. 2011-07-26. Multidimensional semicircular limits on the free Wigner chaos. https://arxiv.org/abs/1107.5135

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