Pseudoisotropic random walks on free groups and semigroups

We present strong laws of large numbers, central limit theorems and laws of the iterated logarithm for the growth of some random walks on free groups and semigroups which generalize isotropic random walks. Our method to derive these results is based on corresponding limit theorems on polynomial hypergroups. If this method can be applied, then it has the advantage that expectation and variance appearing in the limit theorems can be computed explicitly.