Asymptotic geometric analysis. P. 1, Asymptotic geometric analysis, part I / Shiri Artstein-Avidan Apostolos Giannopoulos Vit free ebook download.

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Asymptotic geometric analysis. P. 1, Asymptotic geometric analysis, part I / Shiri Artstein-Avidan Apostolos Giannopoulos Vit free ebook download

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Mathematics

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Catalogue

Author(s):	Shiri Artstein-avidan, Apostolos Giannopoulos, Vitali D. Milman

Date:	2018	Format:	PDF	Language:	English	ISBN/ASIN:	1470421933
Pages:	451	OCR:		Quality:		ISBN13:
Uploader:	Gustavi	Upload Date:	7/12/2019 12:45:24 AM

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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

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Tags: analysis Apostolos Asymptotic geometric part

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