An obstruction for q-deformation of the convolution product
funct-an
2009-10-28 v2 Operator Algebras
Quantum Algebra
q-alg
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.
Cite
@article{arxiv.funct-an/9511002,
title = {An obstruction for q-deformation of the convolution product},
author = {Hans van Leeuwen and Hans Maassen},
journal= {arXiv preprint arXiv:funct-an/9511002},
year = {2009}
}
Comments
The proof of proposition 2 is corrected on 11 january 1996