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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| Format: | Article |
| Language: | English |
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MDPI AG
2009-04-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/11/2/222/ |
| _version_ | 1798024477558177792 |
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| author | Peter Harremoës |
| author_facet | Peter Harremoës |
| author_sort | Peter Harremoës |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-04-11T18:03:04Z |
| format | Article |
| id | doaj.art-744814052b6340e6a2a73fe85a2306b6 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T18:03:04Z |
| publishDate | 2009-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-744814052b6340e6a2a73fe85a2306b62022-12-22T04:10:25ZengMDPI 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 |
| 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 |
| title | 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_short | Maximum Entropy on Compact Groups |
| title_sort | maximum entropy on compact groups |
| 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 |