In addition, the sharp upper bound of the minimal p-mean width ofLp zonoids is obtained

We calculate the upper transform C 2,λ u (f ) for non- smooth convex functions arising from convex programming, such as the maximum function (1.8), and we also use an anisotropic

This was first proved by Comets and Yoshida [3, Theorem 2.4.4], for a model of directed polymers in which the random walk is replaced by a Brownian motion and the environment is

and its generalizations when all the variables are positive definite, bounded, self- adjoint linear operators on a Hilbert space... For example, a very special case

Pinelis, Birkh¨ auser, Basel L’Hospital type rules for monotonicity: applications to probability inequalities for sums of bounded random variables. Pinelis, Binomial upper bounds

The idea is to approximate the infinite dimensional problem by a finite dimensional one, to show convexity of the minimizers of the finite dimensional problems and prove convergence

The sharp bounds for the affine invariant ratio of the mixed cone-volume functional to the Minkowski first mixed volume are obtained, and therefore new affine isoperimetric inequalities

(Böröczky-Lutwak-Yang-Zhang, [4]) A non-zero finite even Borel measure on the unit sphere S n−1 is the cone-volume measure of an origin-symmetric convex body in R n if and only if

This motivates Section 3, where only the substrate is random, and the film is defined as the infimum of a collection of Wulff shapes over the substrate.. In Section 4 we prove