Maximum Entropy on Compact Groups

Details Maximum Entropy on Compact Groups Maximum Entropy on Compact Groups

2008-12-30

arxiv.org/abs/0901.0015v2

Entropy 2009, 11(2), 222-237

Computer Science

Information Theory

Scientific paper

10.3390/e11020222

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.

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