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Entropy 2009, 11(2), 222-237; doi:10.3390/e11020222

Maximum Entropy on Compact Groups

Centrum Wiskunde & Informatica, Science Park 123, 1098 GB Amsterdam, Noord-Holland, The Netherlands
Received: 30 December 2008 / Accepted: 31 March 2009 / Published: 1 April 2009
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Abstract

In 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.
Keywords: Compact group; Convolution; Haar measure; Information divergence; Maximum entropy; Rate distortion function; Rate of convergence; Symmetry Compact group; Convolution; Haar measure; Information divergence; Maximum entropy; Rate distortion function; Rate of convergence; Symmetry
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Harremoës, P. Maximum Entropy on Compact Groups. Entropy 2009, 11, 222-237.

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