Equidistribution of random walks on compact groups II. The Wasserstein metric
Equidistribution of random walks on compact groups II. The Wasserstein metric
We consider a random walk Sk with i.i.d. steps on a compact group equipped with a bi-invariant metric. We prove quantitative ergodic theorems for the sum ∑ k=1Nf(Sk) with Hölder continuous test functions f, including the central limit theorem, the law of the iterated logarithm and an almost sure approximation …