$q$-Chaos

Details $q$-Chaos $q$-Chaos

2008-01-24

arxiv.org/abs/0801.3704v1

Mathematics

Operator Algebras

22 pages

Scientific paper

We consider the $L_p$ norm estimates for homogeneous polynomials of
$q$-gaussian variables ($-1\leq q\leq 1$). When $-1for $1\leq p \leq 2$ are essentially the same as the free case ($q=0$), whilst
the $L_p$ estimates for $2\leq p \leq \infty$ show a strong $q$-dependence.
Moreover, the extremal cases $q = \pm 1$ produce decisively different formulae.

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