Hans van Leeuwen,Hans Maassen
An obstruction for q-deformation of the convolution product
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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.