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Generalized q-deformed Gaussian random variables

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Bożejko M., Yoshida H.

Banach Center Publications

2006

tom 73

nr 1

127-140

We produce generalized q-Gaussian random variables which have two parameters of deformation. One of them is, of course, q as for the usual q-deformation. We also investigate the corresponding Wick formulas, which will be described by some joint statistics on pair partitions.

New limit theorems related to free multiplicative convolution

100%

Sakuma N., Yoshida H.

Studia Mathematica

2013

tom 214

nr 3

251-264

Let ⊞, ⊠, and ⊎ be the free additive, free multiplicative, and boolean additive convolutions, respectively. For a probability measure μ on [0,∞) with finite second moment, we find a scaling limit of $(μ^{⊠ N})^{⊞ N}$ as N goes to infinity. The 𝓡-transform of its limit distribution can be represented by Lambert's W-function. From this, we deduce that the limiting distribution is freely infinitely divisible, like the lognormal distribution in the classical case. We also show a similar limit theorem by replacing free additive convolution with boolean convolution.

Ograniczanie wyników

1 Banach Center Publications

1 Studia Mathematica

2 Yoshida H.

1 Bożejko M.

1 Sakuma N.

1 2013

1 2006

Wyniki wyszukiwania

Generalized q-deformed Gaussian random variables

New limit theorems related to free multiplicative convolution