Central limit theorems for Coxeter systems and Artin systems of extra large type

Details Central limit theorems for Coxeter systems and Artin systems of extra large type Central limit theorems for Coxeter systems and Artin systems of extra large type

2003-11-06

arxiv.org/abs/math/0311076v1

Mathematics

Functional Analysis

12 pages

Scientific paper

Given a Coxeter system of large type we prove a non--commutative central limit theorem: After normalisation with the square root of n the characteristic function of the set of the first n generators tends in distribution to Wigners semi--circle law. If one chooses the group presentation at random, now admitting a certain amount of commutation among the generators, the distributional limit will be the q--deformed semi--circle law, $1\leq q \leq 1$, almost surely.

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