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An obstruction for q-deformation of the convolution product

Hans van Leeuwen·Hans Maassen
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Abstract

We consider two independent q-Gaussian random variables X and Y and a function f chosen in such a way that f(X) and X have the same distribution. For 0 < q < 1 we find that at least the fourth moments of X + Y and f(X) + Y are different. We conclude that no q-deformed convolution product can exist for functions of independent q-Gaussian random variables.

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Hans van Leeuwen, Hans Maassen. 1996-01-11. An obstruction for q-deformation of the convolution product. https://doi.org/10.1088/0305-4470%2F29%2F15%2F036

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