  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.
