Entropy jumps in the presence of a spectral gap
Ball, Keith ; Barthe, Franck ; Naor, Assaf
Duke Math. J., Tome 120 (2003) no. 3, p. 41-63 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
It is shown that if X is a random variable whose density satisfies a Poincaré inequality, and Y is an independent copy of X, then the entropy of (X + Y)/√2 is greater than that of X by a fixed fraction of the entropy gap between X and the Gaussian of the same variance. The argument uses a new formula for the Fisher information of a marginal, which can be viewed as a local, reverse form of the Brunn-Minkowski inequality (in its functional form due to A. Prékopa and L. Leindler).
Publié le : 2003-07-15
Classification:  94A17,  60E15 
@article{1082744705,
     author = {Ball, Keith and Barthe, Franck and Naor, Assaf},
     title = {Entropy jumps in the presence of a spectral gap},
     journal = {Duke Math. J.},
     volume = {120},
     number = {3},
     year = {2003},
     pages = { 41-63},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1082744705}
}

Ball, Keith; Barthe, Franck; Naor, Assaf. Entropy jumps in the presence of a spectral gap. Duke Math. J., Tome 120 (2003) no. 3, pp.  41-63. http://gdmltest.u-ga.fr/item/1082744705/