On Free and Classical Type G Distributions
نویسندگان
چکیده
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 distributions. A new characterization of classical type distributions is given first and the class of type classical infinitely divisible distributions is introduced. The corresponding free type distributions are studied and the role of a special symmetric beta distribution is shown as a building block for free type distributions. It is proved that this symmetric beta distribution is the free multiplicative convolution of an arcsine distribution with the Marchenko-Pastur distribution.
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