### Abstract

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 ineauality (in its functional form due to A. Prékopa and L. Leindler).

Original language | English (US) |
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Pages (from-to) | 41-63 |

Number of pages | 23 |

Journal | Duke Mathematical Journal |

Volume | 119 |

Issue number | 1 |

DOIs | |

State | Published - Jul 15 2003 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

## Fingerprint Dive into the research topics of 'Entropy jumps in the presence of a spectral gap'. Together they form a unique fingerprint.

## Cite this

Ball, K., Barthe, F., & Naor, A. (2003). Entropy jumps in the presence of a spectral gap.

*Duke Mathematical Journal*,*119*(1), 41-63. https://doi.org/10.1215/S0012-7094-03-11912-2