Artstein, S.;
Ball, K.M.;
Barthe, F.;
Naor, A.;
(2004)
Solution of Shannon's problem on the monotonicity of entropy.
Journal of the American Mathematical Society
, 17
(4)
pp. 975-982.
10.1090/S0894-0347-04-00459-X.
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Abstract
It is shown that if X1, X2, . . . are independent and identically distributed square-integrable random variables then the entropy of the normalized sum Ent (X1+ · · · + Xn over √n) is an increasing function of n. This resolves an old problem which goes back to [6, 7, 5]. The result also has a version for non-identically distributed random variables or random vectors.
| Type: | Article |
|---|---|
| Title: | Solution of Shannon's problem on the monotonicity of entropy |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1090/S0894-0347-04-00459-X |
| Publisher version: | http://dx.doi.org/10.1090/S0894-0347-04-00459-X |
| Language: | English |
| UCL classification: | UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/12545 |
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