Softcover ISBN:  9781470463601 
Product Code:  SURV/261 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9781470467777 
Product Code:  SURV/261.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9781470463601 
eBook: ISBN:  9781470467777 
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:  9781470463601 
Product Code:  SURV/261 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9781470467777 
Product Code:  SURV/261.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9781470463601 
eBook ISBN:  9781470467777 
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 

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 logconcave measures, thinshell estimates, stochastic localization, the geometry of Gaussian measures, volume inequalities for convex bodies, local theory of Banach spaces, type and cotype, the BanachMazur 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.

Table of Contents

Chapters

Functional inequalities and concentration of measure

Isoperimetric constants of logconcave measures and related problems

Inequalities for Guassian measures

Volume inequalities

Local theory of finite dimensional normed spaces: Type and cotype

Geometry of the BanachMazur compactum

Asymptotic convex geometry and classical symmetrizations

Restricted invertibility and the KadisonSinger problem

Functionalization of geometry


Additional Material

Reviews

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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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 logconcave measures, thinshell estimates, stochastic localization, the geometry of Gaussian measures, volume inequalities for convex bodies, local theory of Banach spaces, type and cotype, the BanachMazur 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 logconcave measures and related problems

Inequalities for Guassian measures

Volume inequalities

Local theory of finite dimensional normed spaces: Type and cotype

Geometry of the BanachMazur compactum

Asymptotic convex geometry and classical symmetrizations

Restricted invertibility and the KadisonSinger 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