Probability on groups: Random walks and invariant diffusions (Q2756781)

This paper gives a short introduction and survey about recent interesting results and problems on the asymptotic behavior of random walks and Gaussian processes (which are called invariant diffusions in the paper) on groups. A first big topic in this field is the study of the rate of convergence of random walks or Gaussian processes on a compact group to the uniform distribution. Another topic discussed in the paper concerns the asymptotic behavior of random walks and geometric properties of the underlying groups like the validity of a Harnack inequality, polynomial or exponential growth, or amenability.