| Shannon's monotonicity problem for free and classical entropy. | |
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MedLine Citation:
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PMID: 17881587 Owner: NLM Status: MEDLINE |
Abstract/OtherAbstract:
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We give a short unified proof of the following theorem, valid in the context of both classical probability theory and Voiculescu's free probability theory: let (X(j)((1)), ..., X(j)((n))) be independent (resp., freely independent) n-tuples of random variables. Let Z(N)((p)) = N(-1/2)(X(1)((p)) + ... + X(N)((p))) be their central limit sums. Then the entropy (resp., free entropy) of the n-tuple (Z(N)((1)), ..., Z(N)((n))) is a monotone function of N. The classical case (for n = 1) is a celebrated result of Artstein, Ball, Barthe, and Naor, and our proof is an adaptation and simplification of their argument. |
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Authors:
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Dimitri Shlyakhtenko; Hanne Schultz |
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Publication Detail:
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Type: Journal Article; Research Support, U.S. Gov't, Non-P.H.S. Date: 2007-09-19 |
Journal Detail:
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Title: Proceedings of the National Academy of Sciences of the United States of America Volume: 104 ISSN: 0027-8424 ISO Abbreviation: Proc. Natl. Acad. Sci. U.S.A. Publication Date: 2007 Sep |
Date Detail:
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Created Date: 2007-09-26 Completed Date: 2007-10-26 Revised Date: 2011-01-04 |
Medline Journal Info:
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Nlm Unique ID: 7505876 Medline TA: Proc Natl Acad Sci U S A Country: United States |
Other Details:
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Languages: eng Pagination: 15254-8 Citation Subset: IM |
Affiliation:
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Department of Mathematics, University of California, Los Angeles, CA 90095, USA. shlyakht@math.ucla.edu |
Export Citation:
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| MeSH Terms | |
Descriptor/Qualifier:
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Entropy* Information Theory Models, Statistical* Models, Theoretical Normal Distribution Probability |
From MEDLINE®/PubMed®, a database of the U.S. National Library of Medicine
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