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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.
List of contents
Preface.- F. Barthe, M. Csörnyei and A. Naor: A Note on Simultaneous Polar and Cartesian Decomposition.- A. Barvinok: Approximating a Norm by a Polynomial.- S.G. Bobkov: Concentration of Distributions of the Weighted Sums with Bernoullian Coefficients.- S.G. Bobkov: Spectral Gap and Concentration for Some Spherically Symmetric Probability Measures.- S.G. Bobkov and A. Koldobsky: On the Central Limit Property of Convex Bodies.- S.G. Bobkov and F.L. Nazarov: On Convex Bodies and Log-Concave Probability Measures with Unconditional Basis.- J. Bourgain: Random Lattice Schrödinger Operators with Decaying Potential: Some Higher Dimensional Phenomena.- J. Bourgain: On Long-Time Behaviour of Solutions of Linear Schrödinger Equations with Smooth Time-Dependent Potential.- J. Bourgain: On the Isotropy-Constant Problem for 'PSI-2'-Bodies.- E.D. Gluskin: On the Sum of Intervals.- E. Gluskin and V. Milman: Note on the Geometric-Arithmetic Mean Inequality.- O. Guédon and A. Zvavitch: Supremum of a Process in Terms of Trees.- O. Maleva: Point Preimages under Ball Non-Collapsing Mappings.- V. Milman and R. Wagner: Some Remarks on a Lemma of Ran Raz.- F. Nazarov: On the Maximal Perimeter of a Convex Set in R^n with Respect to a Gaussian Measure.- K. Oleszkiewicz: On p-Pseudostable Random Variables, Rosenthal Spaces and l_p^n Ball Slicing.- G. Paouris: Psi_2-Estimates for Linear Functionals on Zonoids.- G. Schechtman, N. Tomczak-Jaegermann and R. Vershynin: Maximal l_p^n-Structures in Spaces with Extremal Parameters.- C. Schütt and E. Werner: Polytopes with Vertices Chosen Randomly from the Boundary of a Convex Body.- Seminar Talks (with Related Workshop and Conference Talks).
Summary
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.
