The normal distribution is -infinitely divisible
arXiv:0910.4263 · doi:10.1016/j.aim.2010.10.025
Abstract
We prove that the classical normal distribution is infinitely divisible with respect to the free additive convolution. We study the Voiculescu transform first by giving a survey of its combinatorial implications and then analytically, including a proof of free infinite divisibility. In fact we prove that a subfamily Askey-Wimp-Kerov distributions are freely infinitely divisible, of which the normal distribution is a special case. At the time of this writing this is only the third example known to us of a nontrivial distribution that is infinitely divisible with respect to both classical and free convolution, the others being the Cauchy distribution and the free 1/2-stable distribution.
AMS LaTeX, 29 pages, using tikz and 3 eps figures; new proof including infinite divisibility of certain Askey-Wilson-Kerov distibutions
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Cited by in corpus (21)
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