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Über dieses Buch

Asymptotic Geometric Analysis is concerned with the geometric and linear properties of finite dimensional objects, normed spaces, and convex bodies, especially with the asymptotics of their various quantitative parameters as the dimension tends to infinity. The deep geometric, probabilistic, and combinatorial methods developed here are used outside the field in many areas of mathematics and mathematical sciences. The Fields Institute Thematic Program in the Fall of 2010 continued an established tradition of previous large-scale programs devoted to the same general research direction. The main directions of the program included:

* Asymptotic theory of convexity and normed spaces

* Concentration of measure and isoperimetric inequalities, optimal transportation approach

* Applications of the concept of concentration

* Connections with transformation groups and Ramsey theory

* Geometrization of probability

* Random matrices

* Connection with asymptotic combinatorics and complexity theory

These directions are represented in this volume and reflect the present state of this important area of research. It will be of benefit to researchers working in a wide range of mathematical sciences—in particular functional analysis, combinatorics, convex geometry, dynamical systems, operator algebras, and computer science.

Inhaltsverzeichnis

Frontmatter

2013 | OriginalPaper | Buchkapitel

The Variance Conjecture on Some Polytopes

David Alonso–Gutiérrez, Jesús Bastero

2013 | OriginalPaper | Buchkapitel

More Universal Minimal Flows of Groups of Automorphisms of Uncountable Structures

Dana Bartošová

2013 | OriginalPaper | Buchkapitel

On the Lyapounov Exponents of Schrödinger Operators Associated with the Standard Map

J. Bourgain

2013 | OriginalPaper | Buchkapitel

Overgroups of the Automorphism Group of the Rado Graph

Peter Cameron, Claude Laflamme, Maurice Pouzet, Sam Tarzi, Robert Woodrow

2013 | OriginalPaper | Buchkapitel

On a Stability Property of the Generalized Spherical Radon Transform

Dmitry Faifman

2013 | OriginalPaper | Buchkapitel

Banach Representations and Affine Compactifications of Dynamical Systems

Eli Glasner, Michael Megrelishvili

2013 | OriginalPaper | Buchkapitel

Flag Measures for Convex Bodies

Daniel Hug, Ines Türk, Wolfgang Weil

2013 | OriginalPaper | Buchkapitel

Operator Functional Equations in Analysis

Hermann König, Vitali Milman

2013 | OriginalPaper | Buchkapitel

A Remark on the Extremal Non-Central Sections of the Unit Cube

James Moody, Corey Stone, David Zach, Artem Zvavitch

2013 | OriginalPaper | Buchkapitel

Universal Flows of Closed Subgroups of S ∞ and Relative Extreme Amenability

L. Nguyen Van Thé

2013 | OriginalPaper | Buchkapitel

Oscillation of Urysohn Type Spaces

N. W. Sauer

2013 | OriginalPaper | Buchkapitel

Euclidean Sections of Convex Bodies

Gideon Schechtman

2013 | OriginalPaper | Buchkapitel

Duality on Convex Sets in Generalized Regions

Alexander Segal, Boaz A. Slomka

2013 | OriginalPaper | Buchkapitel

On Polygons and Injective Mappings of the Plane

Boaz A. Slomka

2013 | OriginalPaper | Buchkapitel

Abstract Approach to Ramsey Theory and Ramsey Theorems for Finite Trees

Sławomir Solecki

2013 | OriginalPaper | Buchkapitel

Some Affine Invariants Revisited

Alina Stancu

2013 | OriginalPaper | Buchkapitel

On the Geometry of Log-Concave Probability Measures with Bounded Log-Sobolev Constant

P. Stavrakakis, P. Valettas

2013 | OriginalPaper | Buchkapitel

f-Divergence for Convex Bodies

Elisabeth M. Werner
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