An obstruction for q-deformation of the convolution product

TL;DR

The paper demonstrates that a q-deformed convolution product cannot be defined for independent q-Gaussian variables by showing differences in moments after certain transformations.

Contribution

It proves the non-existence of a q-deformed convolution for independent q-Gaussian variables through moment analysis.

Findings

Fourth moments of X+Y and f(X)+Y differ for 0<q<1

No q-deformed convolution product can exist for these variables

Transformations do not preserve the convolution structure

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.