F. Barthe, M. Csörnyei, A. Naor (auth.), Vitali D. Milman, Gideon Schechtman (eds.)3540004858, 9783540004851
The proceedings of the Israeli GAFA seminar on Geometric Aspect of Functional Analysis during the years 2001-2002 follow the long tradition of the previous volumes. They continue to reflect the general trends of the Theory. Several papers deal with the slicing problem and its relatives. Some deal with the concentration phenomenon and related topics. In many of the papers there is a deep interplay between Probability and Convexity. The volume contains also a profound study on approximating convex sets by randomly chosen polytopes and its relation to floating bodies, an important subject in Classical Convexity Theory. All the papers of this collection are original research papers.
Table of contents :
A Note on Simultaneous Polar and Cartesian Decomposition….Pages 1-19
Approximating a Norm by a Polynomial….Pages 20-26
Concentration of Distributions of the Weighted Sums with Bernoullian Coefficients….Pages 27-36
Spectral Gap and Concentration for Some Spherically Symmetric Probability Measures….Pages 37-43
On the Central Limit Property of Convex Bodies….Pages 44-52
On Convex Bodies and Log-Concave Probability Measures with Unconditional Basis….Pages 53-69
Random Lattice Schrödinger Operators with Decaying Potential: Some Higher Dimensional Phenomena….Pages 70-98
On Long-Time Behaviour of Solutions of Linear Schrödinger Equations with Smooth Time-Dependent Potential….Pages 99-113
On the Isotropy-Constant Problem for “PSI-2”-Bodies….Pages 114-121
On the Sum of Intervals….Pages 122-130
Note on the Geometric-Arithmetic Mean Inequality….Pages 131-135
Supremum of a Process in Terms of Trees….Pages 136-147
Point Preimages under Ball Non-Collapsing Mappings….Pages 148-157
Some Remarks on a Lemma of Ran Raz….Pages 158-168
On the Maximal Perimeter of a Convex Set in $mathbb{R}^n$ with Respect to a Gaussian Measure….Pages 169-187
On p -Pseudostable Random Variables, Rosenthal Spaces and l p n Ball Slicing….Pages 188-210
$Psi_2$ -Estimates for Linear Functionals on Zonoids….Pages 211-222
Maximal $ell_p^n$ -Structures in Spaces with Extremal Parameters….Pages 223-240
Polytopes with Vertices Chosen Randomly from the Boundary of a Convex Body….Pages 241-422
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