Entropy and convergence on compact groups
The classical theory of convergence of convolutions of probability measures on compact groups has concentrated on proving weak convergence and uniform convergence of densities. The authors investigate the behaviour of the entropy of convolutions of independent random variables on compact groups. They provide an explicit exponential bound on the rate of convergence of entropy to its maximum. They also prove that this type of convergence lies strictly between uniform convergence of densities and weak convergence.
scientific article; zbMATH DE number 1552712
scientific article