(Ebook) Asymptotic Geometric Analysis, Part II by Shiri Artstein-Avidan, Apostolos Giannopoulos, Vitali D. Milman ISBN 9781470463601, 1470463601

(Ebook) Asymptotic Geometric Analysis, Part II by Shiri Artstein-Avidan, Apostolos Giannopoulos, Vitali D. Milman ISBN 9781470463601, 1470463601

Subject categories: • General convexity • Research exposition (monographs, survey articles) pertaining to functional analysis • Normed linear spaces and Banach spaces; Banach lattices • Geometric probability and stochastic geometry • Probabilistic methods in Banach space theory • Geometry and structure of normed linear spaces • Convex sets in n dimensions (including convex hypersurfaces) • Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry) • Asymptotic theory of convex bodies • Inequalities and extremum problems involving convexity in convex geometryThis 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.