Asymptotic Geometric Analysis, Part II
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A01=Apostolos Giannopoulos
A01=Shiri Artstein-Avidan
A01=Vitali D. Milman
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Author_Apostolos Giannopoulos
Author_Shiri Artstein-Avidan
Author_Vitali D. Milman
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Product details
- ISBN 9781470463601
- Weight: 633g
- Dimensions: 178 x 254mm
- Publication Date: 28 Feb 2022
- Publisher: American Mathematical Society
- Publication City/Country: US
- Product Form: Paperback
- Language: English
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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 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.
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.
Shiri Artstein-Avidan, Tel Aviv University, Israel.
Apostolos Giannopoulos, University of Athens, Greece.
Vitali D. Milman, Tel Aviv University, Israel.
Apostolos Giannopoulos, University of Athens, Greece.
Vitali D. Milman, Tel Aviv University, Israel.
