Abstract: In the talk we will consider the following topics: 1. For Coxeter group (W,S) ,let classical length function associated with Coxeter generators is (*) |x| = min{ k : x = s_{1} ...s_{k} , s_{j} are in S } and the block length function is || x || = card { s_{1}, s_{2},..., s_{k} }, i.e. the number of different Coxeter generators in the reduced form (*). We show that above length functions are conditionally negative definite, so for each t>0, exp(-t|x|) and exp(-t||x||) are positive definite on Coxeter group (W,S). Using that and more general positive definite functions(so called Riesz-Coxeter product) we present the ideas of the proofs of the following theorems: 2. The set of Coxeter generators S is Sidon set, i.e. every function f :S into [0,1] ,can be extended to positive definite function of the Coxeter group W. 3. The operator-version of Kchinchine inequalities of Haagerup-Pisier-Buchholz , holds on the set of generators S. 4.The Normal law and q-Gaussian law, 0