Hyperbolic Measures on Infinite Dimensional Spaces
Localization and dilation procedures are discussed for infinite dimensional $α$-concave measures on abstract locally convex spaces (following Borell's hierarchy of hyperbolic measures).
math.PR↗
arXiv subjects
Sergey G. Bobkov
Publications and source records attributed to Sergey G. Bobkov.
Rate of convergence and Edgeworth-type expansion in the entropic central limit theorem
An Edgeworth-type expansion is established for the entropy distance to the class of normal distributions of sums of i.i.d. random variables or vectors, satisfying minimal moment conditions.
math.PR↗
On the problem of reversibility of the entropy power inequality
As was shown recently by the authors, the entropy power inequality can be reversed for independent summands with sufficiently concave densities, when the distributions of the summands are put in a special position. In this note it is proved that reversibility is impossible over the whole class of convex probability distributions. Related phenomena for identically distributed summands are also discussed.
math.FA↗
Berry-Esseen bounds in the entropic central limit theorem
Berry-Esseen-type bounds for total variation and relative entropy distances to the normal law are established for the sums of non-i.i.d. random variables.
math.PR↗
Weighted Poincaré-type inequalities for Cauchy and other convex measures
Brascamp--Lieb-type, weighted Poincaré-type and related analytic inequalities are studied for multidimensional Cauchy distributions and more general $κ$-concave probability measures (in the hierarchy of convex measures). In analogy with the limiting (infinite-dimensional log-concave) Gaussian model, the weighted inequalities fully describe the measure concentration and large deviation properties of this family of measures. Cheeger-type isoperimetric inequalities are investigated similarly, giving rise to a common weight in the class of concave probability measures under consideration.
math.PR↗
Concentration of normalized sums and a central limit theorem for noncorrelated random variables
For noncorrelated random variables, we study a concentration property of the family of distributions of normalized sums formed by sequences of times of a given large length.
math.PR↗