Geodesic
Solution of Shannon’s problem on the monotonicity of entropy
Artstein, Shiri 1   ; Ball, Keith 2   ; Barthe, Franck 3   ; Naor, Assaf 4
1 School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel
2 Department of Mathematics, University College London, Gower Street, London WC1 6BT, United Kingdom
3 Institut de Mathématiques, Laboratoire de Statistique et Probabilités, CNRS UMR C5583, Université Paul Sabatier, 31062 Toulouse Cedex 4, France
4 Theory Group, Microsoft Research, One Microsoft Way, Redmond, Washington 98052-6399
Journal of the American Mathematical Society, Tome 17 (2004) no. 4, pp. 975-982 Cet article a éte moissonné depuis la source American Mathematical Society

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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.
DOI : 10.1090/S0894-0347-04-00459-X

Artstein, Shiri  1   ; Ball, Keith  2   ; Barthe, Franck  3   ; Naor, Assaf  4

1 School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel
2 Department of Mathematics, University College London, Gower Street, London WC1 6BT, United Kingdom
3 Institut de Mathématiques, Laboratoire de Statistique et Probabilités, CNRS UMR C5583, Université Paul Sabatier, 31062 Toulouse Cedex 4, France
4 Theory Group, Microsoft Research, One Microsoft Way, Redmond, Washington 98052-6399 
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Artstein, Shiri; Ball, Keith; Barthe, Franck; Naor, Assaf. Solution of Shannon’s problem on the monotonicity of entropy. Journal of the American Mathematical Society, Tome 17 (2004) no. 4, pp. 975-982. doi: 10.1090/S0894-0347-04-00459-X

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