The normal distribution is -infinitely divisible
By Serban Teodor Belinschi, M. Bożejko, Franz Lehner, Roland Speicher. 2009
48 citations recorded by the source corpus.
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 sub-family of 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.
Subfields: Applied Mathematics, Discrete Mathematics and Combinatorics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/c236973979f33e1cb72891e9a46d3fe9dfdf29ba
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In Applied Mathematics
In Discrete Mathematics and Combinatorics
In Statistics and Probability
Citations in the corpus
- Free Probability and Random Matrices (2014, background): “2) There exists a huge body of results around infinitely divisible and stable laws in the free sense; see, for example, [9, 8, 11, 22, 29, 30, 31, 32, 54, 70, 97, 199].”