Extremal slabs in the cube and the Laplace transform.

DOI10.1016/S0001-8708(02)00055-5zbMath1037.52006MaRDI QIDQ1869023

Franck Barthe, Alexander L. Koldobsky

Publication date: 9 April 2003

Published in: Advances in Mathematics (Search for Journal in Brave)

zbMATH Keywords

Laplace transformlog-concave functionvolume of slab

Mathematics Subject Classification ID

Large deviations (60F10) Length, area, volume and convex sets (aspects of convex geometry) (52A38)

Related Items

A Berry-Esseen type inequality for convex bodies with an unconditional basis, Solution of the propeller conjecture in \(\mathbb R^3\), A note on the extremal non-central sections of the cross-polytope, Stability of polydisc slicing, Volume properties of high-dimensional Orlicz balls, Autour de l'inégalité de Brunn-Minkowski, Probabilistic condition number estimates for real polynomial systems. I: A broader family of distributions, Minimal volume of slabs in the complex cube, A Remark on the Extremal Non-Central Sections of the Unit Cube, A probabilistic approach to the geometry of the \(\ell^n_p\)-ball, Volumes of low-dimensional slabs and sections in the cube, On the volume of non-central sections of a cube, Random vectors satisfying Khinchine–Kahane type inequalities for linear and quadratic forms, Thick sections of convex bodies, Cramér’s Theorem is Atypical, On counterexamples in questions of unique determination of convex bodies, Critical central sections of the cube

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Sections of the unit ball of \(\ell ^ n_ p\)
• On a reverse form of the Brascamp-Lieb inequality
• Best constants in Young's inequality, its converse, and its generalization to more than three functions
• An application of the Fourier transform to sections of star bodies
• The subindependence of coordinate slabs in \(l_p^n\) balls
• On the number of nonreal zeros of real entire functions and the Fourier-Pólya conjecture
• Hyperplane projections of the unit ball of \(\ell_{p}^{n}\)
• A function space large deviation principle for certain stochastic integrals
• Gitterperiodische Punktmengen und Isoperimetrie
• Complements of Lyapunov's inequality
• Slicing Convex Bodies-Bounds for Slice Area in Terms of the Body's Covariance
• Slicing the Cube in R n and Probability (Bounds for the Measure of a Central Cube Slice in R n by Probability Methods)
• The central limit problem for convex bodies
• Probability Inequalities for Sums of Bounded Random Variables
• Properties of Probability Distributions with Monotone Hazard Rate