Geodesic
Convergence of the Poincaré constant
Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 3, pp. 615-620 Cet article a éte moissonné depuis la source Math-Net.Ru

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The Poincaré 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.
Keywords: spectral gap, central limit theorem, Fisher information.
Mots-clés : Poincaré constant 
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O. Johnson. Convergence of the Poincaré constant. Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 3, pp. 615-620. http://geodesic.mathdoc.fr/item/TVP_2003_48_3_a12/

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