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On free and classical type G distributions

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  • Department of Mathematical Sciences
There is a one-to-one correspondence between classical one-dimensional infinitely divisible distributions and free infinitely divisible distributions. In this work we study the free infinitely divisible distributions corresponding to the one-dimensional type G distributions. A new characterization of classical type G distributions is given first and the class of type A classical infinitely divisible distributions is introduced. The corresponding free type A distributions are studied and the role of a special symmetric beta distribution is shown as a building block for free type A distributions. It is proved that this symmetric beta distribution is the free multiplicative convolution of an arcsine distribution with the Marchenko–Pastur distribution.
Original languageEnglish
JournalBrazilian Journal of Probability and Statistics
Pages (from-to)106-127
Number of pages22
Publication statusPublished - 2010

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