Geometric Aspects of Functional Analysis: Israel Seminar 2004–2005

S. Alesker (auth.), Vitali D. Milman, Gideon Schechtman (eds.)9783540720522, 3-540-72052-9

This collection of original papers related to the Israeli GAFA seminar (on Geometric Aspects of Functional Analysis) during the years 2004-2005 follows the long tradition of the previous volumes that reflect the general trends of the Theory and are a source of inspiration for research.

Most of the papers deal with different aspects of the Asymptotic Geometric Analysis, ranging from classical topics in the geometry of convex bodies, to inequalities involving volumes of such bodies or, more generally, log-concave measures, to the study of sections or projections of convex bodies. In many of the papers Probability Theory plays an important role; in some limit laws for measures associated with convex bodies, resembling Central Limit Theorems, are derive and in others probabilistic tools are used extensively. There are also papers on related subjects, including a survey on the behavior of the largest eigenvalue of random matrices and some topics in Number Theory.

Table of contents :
Front Matter….Pages I-VIII
Theory of Valuations on Manifolds, IV. New Properties of the Multiplicative Structure….Pages 1-44
Geometric Applications of Chernoff-Type Estimates….Pages 45-75
A Remark on the Surface Brunn–Minkowski-Type Inequality….Pages 77-79
On Isoperimetric Constants for Log-Concave Probability Distributions….Pages 81-88
A Remark on Quantum Ergodicity for CAT Maps….Pages 89-98
Some Arithmetical Applications of the Sum-Product Theorems in Finite Fields….Pages 99-116
On the Maximal Number of Facets of 0/1 Polytopes….Pages 117-125
A Note on an Observation of G. Schechtman….Pages 127-132
Marginals of Geometric Inequalities….Pages 133-166
Deviation Inequalities on Largest Eigenvalues….Pages 167-219
On the Euclidean Metric Entropy of Convex Bodies….Pages 221-235
Some Remarks on Transportation Cost and Related Inequalities….Pages 237-244
A Comment on the Low-Dimensional Busemann–Petty Problem….Pages 245-253
Random Convex Bodies Lacking Symmetric Projections, Revisited Through Decoupling….Pages 255-263
The Random Version of Dvoretzky’s Theorem in $l_{infty}^n$ ….Pages 265-270
Tail-Sensitive Gaussian Asymptotics for Marginals of Concentrated Measures in High Dimension….Pages 271-295
Decoupling Weakly Dependent Events….Pages 297-303
The Square Negative Correlation Property for Generalized Orlicz Balls….Pages 305-313
Back Matter….Pages 315-332