Geometric Aspects of Functional Analysis [[electronic resource] ] : Israel Seminar 2002-2003 / / edited by Vitali D. Milman, Gideon Schechtman

• Pubblicazione: Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2004
• Edizione: 1st ed. 2004.
• Descrizione fisica: 1 online resource (X, 306 p.)
• Disciplina: 515.732
• Soggetto topico: Functional analysis; Convex geometry ; Discrete geometry; Probabilities; Functional Analysis; Convex and Discrete Geometry; Probability Theory and Stochastic Processes
• Classificazione: 46-06
• Persona (resp. second.): MilmanVitali D; SchechtmanGideon
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di contenuto: Intro -- Title -- Preface -- The Start of GAFA Seminar Notes: Some Memories After 20 Years of Activity -- Contents -- 1 Introduction -- 2 Proof of Theorem 2 -- References -- 0 Introduction -- 1 Background -- 2 Hard Lefschetz Theorem for Even Valuations -- 3 The Case of Odd Valuations -- 4 Hard Lefschetz Theorem for Even Valuations from [A4] -- References -- References -- 1 Introduction -- 2 Decay of Norm for a Single Point -- 3 Decay of Diameter of a Convex Body -- 4 Remarks -- 5 Appendix -- References -- 1 A Construction of the Brenier Map -- 2 The Brunn-Minkowski Inequality -- 3 The Marton-Talagrand Inequality -- References -- 1 Introduction -- 2 The Approximation Argument -- 3 The Continuous Version of the Inequalities -- References -- 1 Introduction -- 2 Proof of the Inverse Brascamp-Lieb Inequality -- 3 The Brascamp-Lieb Inequality -- References -- References -- 1 Introduction -- 2 A Distributional Inequality -- 3 Application to Certain Lattice Schrödinger Operators -- 4 A Continuum Model -- 5 Remark on the IDS of the 1-D Bernoulli Model with Weak Disorder -- References -- 1 Introduction -- 2 Symmetrization -- 2.1 Definition -- 2.2 The Effect of a Symmetrization on the Isotropic Constant -- 3 Use of an M -Ellipsoid -- 4 Proof of the Reduction to Bodies with Finite Volume Ratio -- 4.1 Controlling the Axes of an M -Ellipsoid -- 4.2 Finite Volume Ratio -- 5 The Isotropic Position and an M -Ellipsoid -- 6 Appendix: Concave Functions -- References -- References -- 1 Introduction -- 2 On a Geometric Inequality and the Extremal Properties of Euclidean Balls -- 3 Deviation from l2-Estimate -- 4 Random Cotype 2 Property -- 5 Spherical Uniform Distribution -- 6 Can We Check in a "Reasonable Time" that a Normed Space Is Very Far from Euclidean? -- References -- 1 Introduction. ; 2 Tight Embeddings of Euclidean Spaces in Symmetric Spaces and of Symmetric Spaces in Spaces -- 3 Complemented Subspaces of with Unconditional Bases -- References -- 1 Introduction -- 2 Uniqueness -- 3 Extremality Conditions -- 4 Different Bodies Have Different Maps -- 5 Various Optimization Problems -- References -- 0 Introduction -- 1 Definitions and Notations -- 2 The Minimal Volume Ellipsoid of a Symmetric Convex Body -- 3 Convex Bodies in M-Position -- 4 Main Results in the Non-symmetric Case -- 5 Technical Remarks and Improvements -- 6 The Symmetric Quasi-Convex Case -- References -- 1 Introduction -- 2 A General Scheme -- 3 Asymptotic Lower Bound for dist -- 4 The 2-Dimensional Case -- References -- 1 Introduction -- 2 Glivenko-Cantelli Classes and Learnability -- 2.1 The Classical Approach -- 2.2 Talagrand's Inequality for Empirical Processes -- 3 Uniform Measures of Complexity -- 3.1 Metric Entropy and the Combinatorial Dimension -- 3.2 Random Averages and the Combinatorial Dimension -- 3.3 Phase Transitions in GC Classes -- 3.4 Concentration of the Combinatorial Dimension -- 4 Learning Sample Complexity and Error Bounds -- 4.1 Error Bounds -- 4.2 Comparing Structures -- 5 Estimating the Localized Averages -- 5.1 Localized Averages -- 5.2 Data Dependent Bounds -- 5.3 Geometric Interpretation -- 6 Bernstein Type of Loss Classes -- 7 Classes of Linear Functionals -- 8 Concluding Remarks -- References -- 1 Introduction -- 2 Essential Uniqueness of M -Ellipsoids -- References -- 1 Frameworks and Models -- 1.1 Generalities -- 1.2 Interactions -- 1.3 Thermodynamic Limit of the Ground State Energy -- 2 Thermodynamic Limit in the Case of Short Range Interaction -- 3 Thermodynamic Limit for Mean Field Type Models -- 3.1 Weak Selfaveraging Property -- 3.2 Strong Selfaveraging Property of the Free Energy. ; 4 Two Simple Models with Phase Transitions -- 4.1 Kac Model -- 4.2 Spherical Model -- 4.3 Concluding Remarks on Phase Transitions -- References -- References -- 1 Introduction -- 2 Proof of the Theorem -- References -- Israel GAFA Seminar (2002-2004) -- PIMS Thematic Programme on Asymptotic Geometric Analysis at the University of British Columbia (Summer 2002) -- Conference on Convexity and Asymptotic Theory of Normed Spaces -- Concentration Period on Measure Transportation and Geometric Inequalities -- Conference on Phenomena of Large Dimensions -- Conference on Non-commutative Phenomena and Random Matrices -- Conference on Banach Spaces -- Banach Spaces and Convex Geometric Analysis (April, 2003) -- Paris GAFA Seminar (Summer 2003) -- GAFA Session Joint Meeting of the New Zealand Mathematical Society and Israel Mathematical Union (Wellington, February 2004).
• Sommario/riassunto: 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.
• Titolo autorizzato: Geometric aspects of functional analysis
• ISBN: 3-540-44489-0
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 996466483903316
• Lo trovi qui: Univ. di Salerno
• Serie: Lecture Notes in Mathematics, . 0075-8434 ; ; 1850