Geometric Aspects of Functional Analysis: Israel Seminar 2002-2003

Vitali D. Milman, Gideon Schechtman (auth.)3540223606, 9783540223603

The Israeli GAFA seminar (on Geometric Aspect of Functional Analysis) during the years 2002-2003 follows the long tradition of the previous volumes. It reflects the general trends of the theory. Most of the papers deal with different aspects of the Asymptotic Geometric Analysis. In addition the volume contains papers on related aspects of Probability, classical Convexity and also Partial Differential Equations and Banach Algebras. There are also two expository papers on topics which proved to be very much related to the main topic of the seminar. One is Statistical Learning Theory and the other is Models of Statistical Physics. All the papers of this collection are original research papers.

Table of contents :
A Topological Obstruction to Existence of Quaternionic Plücker Map….Pages 1-7
Hard Lefschetz Theorem for Valuations and Related Questions of Integral Geometry….Pages 9-20
SU (2)-Invariant Valuations….Pages 21-29
The Change in the Diameter of a Convex Body under a Random Sign-Projection….Pages 31-39
An Elementary Introduction to Monotone Transportation….Pages 41-52
A Continuous Version of the Brascamp-Lieb Inequalities….Pages 53-63
Inverse Brascamp-Lieb Inequalities along the Heat Equation….Pages 65-71
Pinched Exponential Volume Growth Implies an Infinite Dimensional Isoperimetric Inequality….Pages 73-76
On Localization for Lattice Schrödinger Operators Involving Bernoulli Variables….Pages 77-99
Symmetrization and Isotropic Constants of Convex Bodies….Pages 101-115
On the Multivariable Version of Ball’s Slicing Cube Theorem….Pages 117-121
Geometric Probability and Random Cotype 2….Pages 123-138
Several Remarks Concerning the Local Theory of L p Spaces….Pages 139-148
On John-Type Ellipsoids….Pages 149-158
Isomorphic Random Subspaces and Quotients of Convex and Quasi-Convex Bodies….Pages 159-178
Almost Euclidean Subspaces of Real $ell_p^n$ with p an Even Integer….Pages 179-192
Geometric Parameters in Learning Theory….Pages 193-235
Essential Uniqueness of an M -Ellipsoid of a Given Convex Body….Pages 237-241
On the Thermodynamic Limit for Disordered Spin Systems….Pages 243-268
On Read’s Proof that $B(ell_1)$ Is Not Amenable….Pages 269-275
An Isomorphic Version of the Busemann-Petty Problem for Gaussian Measure….Pages 277-283