$𝜓_{𝛼}$-estimates for marginals of log-concave probability measures
نویسندگان
چکیده
منابع مشابه
Small ball probability estimates for log-concave measures
We establish a small ball probability inequality for isotropic log-concave probability measures: there exist absolute constants c1, c2 > 0 such that if X is an isotropic log-concave random vector in R with ψ2 constant bounded by b and if A is a non-zero n × n matrix, then for every ε ∈ (0, c1) and y ∈ R, P (‖Ax− y‖2 6 ε‖A‖HS) 6 ε ` c2 b ‖A‖HS ‖A‖op ́2 , where c1, c2 > 0 are absolute constants.
متن کاملFunctional Inequalities for Gaussian and Log-Concave Probability Measures
We give three proofs of a functional inequality for the standard Gaussian measure originally due to William Beckner. The first uses the central limit theorem and a tensorial property of the inequality. The second uses the Ornstein-Uhlenbeck semigroup, and the third uses the heat semigroup. These latter two proofs yield a more general inequality than the one Beckner originally proved. We then ge...
متن کاملA ug 2 01 1 Inner Regularization of Log - Concave Measures and Small - Ball Estimates
In the study of concentration properties of isotropic log-concave measures, it is often useful to first ensure that the measure has super-Gaussian marginals. To this end, a standard preprocessing step is to convolve with a Gaussian measure, but this has the disadvantage of destroying small-ball information. We propose an alternative preprocessing step for making the measure seem super-Gaussian,...
متن کاملGaussian Marginals of Probability Measures with Geometric Symmetries
Let K be a convex body in the Euclidean space Rn, n ≥ 2, equipped with its standard inner product 〈·, ·〉 and Euclidean norm | · |. Consider K as a probability space equipped with its uniform (normalized Lebesgue) measure μ. We are interested in k-dimensional marginals of μ, that is, the push-forward μ◦P−1 E of μ by the orthogonal projection PE onto a k-dimensional subspace E ⊂ Rn. The question ...
متن کاملRepresentation of Concave Functions by Radon Probability Measures
Abstract. The aim of this paper is to represent given sets of concave functions by Radon probability measures. We define sets Kp (for p ∈ [1,∞]) of concave functions from the spaces L((0, 1)) having some additional properties. These sets of functions are convex and compact so that Choquet’s theorem can be used to obtain existence of representing measures. Uniqueness is examined on a case-by-cas...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2012
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-2011-10984-5