Maximum Entropy on Compact Groups

Entropy

关键词: Compact group;    Convolution;    Haar measure;    Information divergence;    Maximum entropy;    Rate distortion function;    Rate of convergence;    Symmetry;   

DOI  :  10.3390/e11020222

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2009 by the authors; licensee Molecular Diversity Preservation International, Basel, Switzerland.