Maximum Entropy on Compact Groups

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 entr...

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Main Author:	Peter Harremoës
Format:	Article
Language:	English
Published:	MDPI AG 2009-04-01
Series:	Entropy
Subjects:	Compact group Convolution Haar measure Information divergence Maximum entropy Rate distortion function Rate of convergence Symmetry
Online Access:	http://www.mdpi.com/1099-4300/11/2/222/

id	doaj-744814052b6340e6a2a73fe85a2306b6
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spelling	doaj-744814052b6340e6a2a73fe85a2306b62020-11-24T23:58:49ZengMDPI AGEntropy1099-43002009-04-0111222223710.3390/e11020222Maximum Entropy on Compact GroupsPeter HarremoësIn 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. http://www.mdpi.com/1099-4300/11/2/222/Compact groupConvolutionHaar measureInformation divergenceMaximum entropyRate distortion functionRate of convergenceSymmetry
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Peter Harremoës
spellingShingle	Peter Harremoës Maximum Entropy on Compact Groups Entropy Compact group Convolution Haar measure Information divergence Maximum entropy Rate distortion function Rate of convergence Symmetry
author_facet	Peter Harremoës
author_sort	Peter Harremoës
title	Maximum Entropy on Compact Groups
title_short	Maximum Entropy on Compact Groups
title_full	Maximum Entropy on Compact Groups
title_fullStr	Maximum Entropy on Compact Groups
title_full_unstemmed	Maximum Entropy on Compact Groups
title_sort	maximum entropy on compact groups
publisher	MDPI AG
series	Entropy
issn	1099-4300
publishDate	2009-04-01
description	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.
topic	Compact group Convolution Haar measure Information divergence Maximum entropy Rate distortion function Rate of convergence Symmetry
url	http://www.mdpi.com/1099-4300/11/2/222/
work_keys_str_mv	AT peterharremoes maximumentropyoncompactgroups
_version_	1725449718138404864

Maximum Entropy on Compact Groups

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