## Abstract

The Poincare constant R-Y of a random variable Y relates the L-2(Y)-norm of a function g and its derivative g'. Since R-Y - D(Y) is positive, with equality if and only if Y is normal; it can be seen as a distance from the normal distribution. In this paper we establish the best possible rate of convergence of this distance in the central limit theorem. Furthermore, we show that R-Y is finite for discrete mixtures of normals, allowing us to add rates to the proof of the central limit theorem in the sense of relative entropy.

Translated title of the contribution | Convergence of the Poincare constant |
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Original language | English |

Pages (from-to) | 535 - 541 |

Number of pages | 7 |

Journal | Theory of Probability and its Applications |

Volume | 48 (3) |

DOIs | |

Publication status | Published - 2003 |