Maximum Entropy on Compact Groups

TL;DR

This paper explores entropy and rate distortion theory on compact groups, demonstrating exponential convergence of entropy to its maximum using information theory and Markov chains, with new simplified proofs and results.

Contribution

It introduces new simplified proofs and results on the convergence of convolutions and entropy on compact groups, linking rate distortion functions to entropy increase.

Findings

Entropy converges exponentially to maximum on compact groups

New simplified proofs for convolution convergence

Rate distortion functions characterize entropy increase

Abstract

On a compact group the Haar probability measure plays the role of uniform distribution. The entropy and rate distortion theory for this uniform distribution is studied. New results and simplified proofs on convergence of convolutions on compact groups are presented and they can be formulated as entropy increases to its maximum. Information theoretic techniques and Markov chains play a crucial role. The convergence results are also formulated via rate distortion functions. The rate of convergence is shown to be exponential.