Maximum Entropy on Compact Groups

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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Bibliographic Details
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/
Description
Summary: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.
ISSN:1099-4300

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