Asymptotic Geometric Analysis (Mathematical Surveys and Monographs)

Shiri Artstein-avidan; Apostolos Giannopoulos; Vitali D. Milman

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The authors present the theory of asymptotic geometric analysis, a field which lies on the border between geometry and functional analysis. In this field, isometric problems that are typical for geometry in low dimensions are substituted by an "isomorphic" point of view, and an asymptotic approach (as dimension tends to infinity) is introduced. Geometry and analysis meet here in a non-trivial way. Basic examples of geometric inequalities in isomorphic form which are encountered in the book are the "isomorphic isoperimetric inequalities" which led to the discovery of the "concentration phenomenon", one of the most powerful tools of the theory, responsible for many counterintuitive results. A central theme in this book is the interaction of randomness and pattern. At first glance, life in high dimension seems to mean the existence of multiple "possibilities", so one may expect an increase in the diversity and complexity as dimension increases. However, the concentration of measure and effects caused by convexity show that this diversity is compensated and order and patterns are created for arbitrary convex bodies in the mixture caused by high dimensionality. The book is intended for graduate students and researchers who want to learn about this exciting subject. Among the topics covered in the book are convexity, concentration phenomena, covering numbers, Dvoretzky-type theorems, volume distribution in convex bodies, and more.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

From the Back Cover :

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.

Shiri Artstein-Avidan , Tel Aviv University, Israel. Apostolos Giannopoulos , University of Athens, Greece. Vitali D. Milman , Tel Aviv University, Israel.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

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1.Asymptotic Geometric Analysis: Part I (Hardback)

Edité par American Mathematical Society, United States (2015)
ISBN 10 : 1470421933 ISBN 13 : 9781470421939
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Description du livre American Mathematical Society, United States, 2015. Hardback. État : New. Language: English . Brand New Book. The authors present the theory of asymptotic geometric analysis, a field which lies on the border between geometry and functional analysis. In this field, isometric problems that are typical for geometry in low dimensions are substituted by an isomorphic point of view, and an asymptotic approach (as dimension tends to infinity) is introduced. Geometry and analysis meet here in a non-trivial way. Basic examples of geometric inequalities in isomorphic form which are encountered in the book are the isomorphic isoperimetric inequalities which led to the discovery of the concentration phenomenon , one of the most powerful tools of the theory, responsible for many counterintuitive results. A central theme in this book is the interaction of randomness and pattern. At first glance, life in high dimension seems to mean the existence of multiple possibilities , so one may expect an increase in the diversity and complexity as dimension increases. However, the concentration of measure and effects caused by convexity show that this diversity is compensated and order and patterns are created for arbitrary convex bodies in the mixture caused by high dimensionality.The book is intended for graduate students and researchers who want to learn about this exciting subject. Among the topics covered in the book are convexity, concentration phenomena, covering numbers, Dvoretzky-type theorems, volume distribution in convex bodies, and more. N° de réf. du libraire AAN9781470421939

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2.Asymptotic Geometric Analysis: Part I

Edité par American Mathematical Society (2015)
ISBN 10 : 1470421933 ISBN 13 : 9781470421939
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Description du livre American Mathematical Society, 2015. HRD. État : New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. N° de réf. du libraire CE-9781470421939

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3.Asymptotic Geometric Analysis: Part I (Hardback)

Edité par American Mathematical Society, United States (2015)
ISBN 10 : 1470421933 ISBN 13 : 9781470421939
Neuf(s) Couverture rigide Quantité : 1
Vendeur
The Book Depository US
(London, Royaume-Uni)
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Description du livre American Mathematical Society, United States, 2015. Hardback. État : New. Language: English . Brand New Book. The authors present the theory of asymptotic geometric analysis, a field which lies on the border between geometry and functional analysis. In this field, isometric problems that are typical for geometry in low dimensions are substituted by an isomorphic point of view, and an asymptotic approach (as dimension tends to infinity) is introduced. Geometry and analysis meet here in a non-trivial way. Basic examples of geometric inequalities in isomorphic form which are encountered in the book are the isomorphic isoperimetric inequalities which led to the discovery of the concentration phenomenon , one of the most powerful tools of the theory, responsible for many counterintuitive results. A central theme in this book is the interaction of randomness and pattern. At first glance, life in high dimension seems to mean the existence of multiple possibilities , so one may expect an increase in the diversity and complexity as dimension increases. However, the concentration of measure and effects caused by convexity show that this diversity is compensated and order and patterns are created for arbitrary convex bodies in the mixture caused by high dimensionality.The book is intended for graduate students and researchers who want to learn about this exciting subject. Among the topics covered in the book are convexity, concentration phenomena, covering numbers, Dvoretzky-type theorems, volume distribution in convex bodies, and more. N° de réf. du libraire AAN9781470421939

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4.Asymptotic Geometric Analysis: Part I

Edité par American Mathematical Society
ISBN 10 : 1470421933 ISBN 13 : 9781470421939
Neuf(s) Couverture rigide Quantité : 1
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THE SAINT BOOKSTORE
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Description du livre American Mathematical Society. Hardback. État : new. BRAND NEW, Asymptotic Geometric Analysis: Part I, Shiri Artstein-Avidan, Apostolos Giannopoulos, Vitali D. Milman, The authors present the theory of asymptotic geometric analysis, a field which lies on the border between geometry and functional analysis. In this field, isometric problems that are typical for geometry in low dimensions are substituted by an "isomorphic" point of view, and an asymptotic approach (as dimension tends to infinity) is introduced. Geometry and analysis meet here in a non-trivial way. Basic examples of geometric inequalities in isomorphic form which are encountered in the book are the "isomorphic isoperimetric inequalities" which led to the discovery of the "concentration phenomenon", one of the most powerful tools of the theory, responsible for many counterintuitive results. A central theme in this book is the interaction of randomness and pattern. At first glance, life in high dimension seems to mean the existence of multiple "possibilities", so one may expect an increase in the diversity and complexity as dimension increases. However, the concentration of measure and effects caused by convexity show that this diversity is compensated and order and patterns are created for arbitrary convex bodies in the mixture caused by high dimensionality. The book is intended for graduate students and researchers who want to learn about this exciting subject. Among the topics covered in the book are convexity, concentration phenomena, covering numbers, Dvoretzky-type theorems, volume distribution in convex bodies, and more. N° de réf. du libraire B9781470421939

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5.Asymptotic Geometric Analysis

Edité par Amer Mathematical Society (2015)
ISBN 10 : 1470421933 ISBN 13 : 9781470421939
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Description du livre Amer Mathematical Society, 2015. Hardcover. État : Brand New. 451 pages. 10.25x7.50x1.25 inches. In Stock. N° de réf. du libraire __1470421933

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6.Asymptotic Geometric Analysis (Mathematical Surveys and Monographs)

Edité par American Mathematical Society (2015)
ISBN 10 : 1470421933 ISBN 13 : 9781470421939
Neuf(s) Couverture rigide Quantité : 1
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Irish Booksellers
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Description du livre American Mathematical Society, 2015. Hardcover. État : New. book. N° de réf. du libraire 1470421933

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