| Softcover ISBN: | 978-1-4704-6360-1 |
| Product Code: | SURV/261 |
| List Price: | $125.00 |
| MAA Member Price: | $112.50 |
| AMS Member Price: | $100.00 |
| eBook ISBN: | 978-1-4704-6777-7 |
| Product Code: | SURV/261.E |
| List Price: | $125.00 |
| MAA Member Price: | $112.50 |
| AMS Member Price: | $100.00 |
| Softcover ISBN: | 978-1-4704-6360-1 |
| eBook: ISBN: | 978-1-4704-6777-7 |
| Product Code: | SURV/261.B |
| List Price: | $250.00 $187.50 |
| MAA Member Price: | $225.00 $168.75 |
| AMS Member Price: | $200.00 $150.00 |
| Softcover ISBN: | 978-1-4704-6360-1 |
| Product Code: | SURV/261 |
| List Price: | $125.00 |
| MAA Member Price: | $112.50 |
| AMS Member Price: | $100.00 |
| eBook ISBN: | 978-1-4704-6777-7 |
| Product Code: | SURV/261.E |
| List Price: | $125.00 |
| MAA Member Price: | $112.50 |
| AMS Member Price: | $100.00 |
| Softcover ISBN: | 978-1-4704-6360-1 |
| eBook ISBN: | 978-1-4704-6777-7 |
| Product Code: | SURV/261.B |
| List Price: | $250.00 $187.50 |
| MAA Member Price: | $225.00 $168.75 |
| AMS Member Price: | $200.00 $150.00 |
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Book DetailsMathematical Surveys and MonographsVolume: 261; 2021; 645 ppMSC: Primary 52; 46; 60
This book is a continuation of Asymptotic Geometric Analysis, Part I, which was published as volume 202 in this series.
Asymptotic geometric analysis studies properties of geometric objects, such as normed spaces, convex bodies, or convex functions, when the dimensions of these objects increase to infinity. The asymptotic approach reveals many very novel phenomena which influence other fields in mathematics, especially where a large data set is of main concern, or a number of parameters which becomes uncontrollably large. One of the important features of this new theory is in developing tools which allow studying high parametric families.
Among the topics covered in the book are measure concentration, isoperimetric constants of log-concave measures, thin-shell estimates, stochastic localization, the geometry of Gaussian measures, volume inequalities for convex bodies, local theory of Banach spaces, type and cotype, the Banach-Mazur compactum, symmetrizations, restricted invertibility, and functional versions of geometric notions and inequalities.
ReadershipGraduate students and researchers interested in analysis and geometry of high dimensional spaces.
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Table of Contents
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Chapters
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Functional inequalities and concentration of measure
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Isoperimetric constants of log-concave measures and related problems
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Inequalities for Guassian measures
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Volume inequalities
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Local theory of finite dimensional normed spaces: Type and cotype
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Geometry of the Banach-Mazur compactum
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Asymptotic convex geometry and classical symmetrizations
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Restricted invertibility and the Kadison-Singer problem
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Functionalization of geometry
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Additional Material
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Reviews
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The book is very well written, and proofs of the theorems are presented in a most natural and accessible way. Moreover, one can see the authors' fresh and personal touch on many of them. Geometric, analytic and probabilistic views are given in parallel and connections between those subjects are beautifully presented. The book is simply pleasant to read and easy to navigate. After each chapter the authors give a good list of notes with all possible references, which definitely helps with further reading and study. The book contains an outstanding collection of references, which in itself is a great treasure. Thus the book, and indeed the series, provide an excellent source for specialists working in the field as well as for people who wish to join the game and for graduate students.
Artem Zvavitch (Weizmann Institute of Science), MathSciNet
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RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Reviews
- Requests
This book is a continuation of Asymptotic Geometric Analysis, Part I, which was published as volume 202 in this series.
Asymptotic geometric analysis studies properties of geometric objects, such as normed spaces, convex bodies, or convex functions, when the dimensions of these objects increase to infinity. The asymptotic approach reveals many very novel phenomena which influence other fields in mathematics, especially where a large data set is of main concern, or a number of parameters which becomes uncontrollably large. One of the important features of this new theory is in developing tools which allow studying high parametric families.
Among the topics covered in the book are measure concentration, isoperimetric constants of log-concave measures, thin-shell estimates, stochastic localization, the geometry of Gaussian measures, volume inequalities for convex bodies, local theory of Banach spaces, type and cotype, the Banach-Mazur compactum, symmetrizations, restricted invertibility, and functional versions of geometric notions and inequalities.
Graduate students and researchers interested in analysis and geometry of high dimensional spaces.
-
Chapters
-
Functional inequalities and concentration of measure
-
Isoperimetric constants of log-concave measures and related problems
-
Inequalities for Guassian measures
-
Volume inequalities
-
Local theory of finite dimensional normed spaces: Type and cotype
-
Geometry of the Banach-Mazur compactum
-
Asymptotic convex geometry and classical symmetrizations
-
Restricted invertibility and the Kadison-Singer problem
-
Functionalization of geometry
-
The book is very well written, and proofs of the theorems are presented in a most natural and accessible way. Moreover, one can see the authors' fresh and personal touch on many of them. Geometric, analytic and probabilistic views are given in parallel and connections between those subjects are beautifully presented. The book is simply pleasant to read and easy to navigate. After each chapter the authors give a good list of notes with all possible references, which definitely helps with further reading and study. The book contains an outstanding collection of references, which in itself is a great treasure. Thus the book, and indeed the series, provide an excellent source for specialists working in the field as well as for people who wish to join the game and for graduate students.
Artem Zvavitch (Weizmann Institute of Science), MathSciNet
