Skip to Main Content

Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Solution of Shannon’s problem on the monotonicity of entropy
HTML articles powered by AMS MathViewer

by Shiri Artstein, Keith M. Ball, Franck Barthe and Assaf Naor
J. Amer. Math. Soc. 17 (2004), 975-982
DOI: https://doi.org/10.1090/S0894-0347-04-00459-X
Published electronically: May 12, 2004

Abstract:

It is shown that if $X_1,X_2,\ldots$ are independent and identically distributed square-integrable random variables, then the entropy of the normalized sum \[ \operatorname {Ent} \left (\frac {X_{1}+\cdots + X_{n}}{\sqrt {n}} \right ) \] is an increasing function of $n$. The result also has a version for non-identically distributed random variables or random vectors.
References
Similar Articles
  • Retrieve articles in Journal of the American Mathematical Society with MSC (2000): 94A17
  • Retrieve articles in all journals with MSC (2000): 94A17
Bibliographic Information
  • Shiri Artstein
  • Affiliation: School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel
  • Email: artst@post.tau.ac.il
  • Keith M. Ball
  • Affiliation: Department of Mathematics, University College London, Gower Street, London WC1 6BT, United Kingdom
  • Email: kmb@math.ucl.ac.uk
  • Franck Barthe
  • Affiliation: Institut de Mathématiques, Laboratoire de Statistique et Probabilités, CNRS UMR C5583, Université Paul Sabatier, 31062 Toulouse Cedex 4, France
  • MR Author ID: 368041
  • Email: barthe@math.ups-tlse.fr
  • Assaf Naor
  • Affiliation: Theory Group, Microsoft Research, One Microsoft Way, Redmond, Washington 98052-6399
  • Email: anaor@microsoft.com
  • Received by editor(s): September 4, 2003
  • Published electronically: May 12, 2004
  • Additional Notes: The first author was supported in part by the EU Grant HPMT-CT-2000-00037, The Minkowski Center for Geometry and the Israel Science Foundation
    The second author was supported in part by NSF Grant DMS-9796221
    The third author was supported in part by EPSRC Grant GR/R37210
    The last author was supported in part by the BSF, Clore Foundation and EU Grant HPMT-CT-2000-00037
  • © Copyright 2004 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 17 (2004), 975-982
  • MSC (2000): Primary 94A17
  • DOI: https://doi.org/10.1090/S0894-0347-04-00459-X
  • MathSciNet review: 2083473