Displaying similar documents to “On some conjecture concerning Gaussian measures of dilatations of convex symmetric sets”

Tail and moment estimates for some types of chaos

Rafał Latała (1999)

Studia Mathematica

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Let X i be a sequence of independent symmetric real random variables with logarithmically concave tails. We consider a variable X = ∑ i ≠ j a i , j X i X j , where a i , j are real numbers. We derive approximate formulas for the tails and moments of X and of its decoupled version, which are exact up to some universal constants.

The symmetric property ( τ ) for the Gaussian measure

Joseph Lehec (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

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We give a proof, based on the Poincaré inequality, of the symmetric property ( τ ) for the Gaussian measure. If f : ℝ d → ℝ is continuous, bounded from below and even, we define H f ( x ) = inf y f ( x + y ) + 1 2 | y | 2 and we have ∫ e - f d γ d ∫ e H f d γ d ≤ 1 . This property is equivalent to a certain functional form of the Blaschke-Santaló inequality, as explained in a paper by Artstein, Klartag and Milman.

Multivariate normal approximation using Stein’s method and Malliavin calculus

Ivan Nourdin, Giovanni Peccati, Anthony Réveillac (2010)

Annales de l'I.H.P. Probabilités et statistiques

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We combine Stein’s method with Malliavin calculus in order to obtain explicit bounds in the multidimensional normal approximation (in the Wasserstein distance) of functionals of gaussian fields. Among several examples, we provide an application to a functional version of the Breuer–Major CLT for fields subordinated to a fractional brownian motion.