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Multidimensional semicircular limits on the free Wigner chaos
Convergence in Distribution Fourth Moment Condition Free BrownianMotion Free Probability Multidimensional Limit Theorems
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2011/9/21
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...
Wigner Chaos and the Fourth Moment
Wigner Chaos the Fourth Moment
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2010/12/9
We prove that a normalized sequence of multiple Wigner integrals (in a fixed order of free Wigner chaos) converges in law to the standard semicircular distribution if and only if the corresponding seq...