Asymptotic geometric analysis

by Artstein-Avidan, Shiri

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Title Statements

Full title :Asymptotic geometric analysis. / Shiri Artstein-Avidan, Apostolos Giannopoulos, Vitali D. Milman.

Summary

"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."

Edition Statements

Publication Date:©2021

Publication Statements

Publisher(s):American mathematical Society
Place of Publication:Providence, Rhode Island
Language:eng
Publication Date:©2021

The Physical Object

Description:xxxvii, 645 pages : : illustrations ; : 26 cm.

Edition Identifiers

ISBN:1470463601, 9781470463601
oclc:on1285557340
LC Classification:QA360
Dewey Decimal:515.15

Functional inequalities and concentration of measure -- Isoperimetric constants of log-concave measures and related problems -- Inequalities for Gaussian 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.