Displaying similar documents to “The symmetric property ( τ ) for the Gaussian measure”

On some conjecture concerning Gaussian measures of dilatations of convex symmetric sets

Stanisław Kwapień, Jerzy Sawa (1993)

Studia Mathematica

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The paper deals with the following conjecture: if μ is a centered Gaussian measure on a Banach space F,λ > 1, K ⊂ F is a convex, symmetric, closed set, P ⊂ F is a symmetric strip, i.e. P = {x ∈ F : |x'(x)| ≤ 1} for some x' ∈ F', such that μ(K) = μ(P) then μ(λK) ≥ μ(λP). We prove that the conjecture is true under the additional assumption that K is "sufficiently symmetric" with respect to μ, in particular it is true when K is a ball in Hilbert space. As an application we give estimates...

Surface measures and convergence of the Ornstein-Uhlenbeck semigroup in Wiener spaces

Luigi Ambrosio, Alessio Figalli (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

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We study points of density 1 / 2 of sets of finite perimeter in infinite-dimensional Gaussian spaces and prove that, as in the finite-dimensional theory, the surface measure is concentrated on this class of points. Here density 1 / 2 is formulated in terms of the pointwise behaviour of the Ornstein-Uhlembeck semigroup.

On some vector balancing problems

Apostolos Giannopoulos (1997)

Studia Mathematica

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Let V be an origin-symmetric convex body in ℝ n , n≥ 2, of Gaussian measure γ n ( V ) ≥ 1 / 2 . It is proved that for every choice u 1 , . . . , u n of vectors in the Euclidean unit ball B n , there exist signs ε j ∈ - 1 , 1 with ε 1 u 1 + . . . + ε n u n ∈ ( c l o g n ) V . The method used can be modified to give simple proofs of several related results of J. Spencer and E. D. Gluskin.

On Measure Concentration of Vector-Valued Maps

Michel Ledoux, Krzysztof Oleszkiewicz (2007)

Bulletin of the Polish Academy of Sciences. Mathematics

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We study concentration properties for vector-valued maps. In particular, we describe inequalities which capture the exact dimensional behavior of Lipschitz maps with values in ℝ k . To this end, we study in particular a domination principle for projections which might be of independent interest. We further compare our conclusions with earlier results by Pinelis in the Gaussian case, and discuss extensions to the infinite-dimensional setting.