Asymptotic geometric analysis
著者
書誌事項
Asymptotic geometric analysis
（Mathematical surveys and monographs, v. 261）
American Mathematical Society, c2021
- pt. 2
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注記
Includes bibliographical references (p. 595-627) and indexes
内容説明・目次
内容説明
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.
目次
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
Bibliography
Subject index
Author index
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