Asymptotic theory of finite dimensional normed spaces
By: Vitali D. Milman, Gideon Schechtman ; with an appendix by M. Gromov.
Contributors: Schechtman, Gideon, 1947-
Series: Lecture notes in mathematics ;; 1200; Lecture notes in mathematics (Springer-Verlag) ;; 1200.
Publisher: Springer-Verlag
Published: 1986
Place of publication: Berlin; New York
Language: eng
Number of pages: 156
Subjects: Normed linear spaces; Convex sets; Limit theorems (Probability theory)
Description: Vol. 1200 of the LNM series deals with the geometrical structure of finite dimensional normed spaces. One of the main topics is the estimation of the dimensions of euclidean and l n p spaces which nicely embed into diverse finite-dimensional normed spaces. An essential method here is the concentration of measure phenomenon which is closely related to large deviation inequalities in Probability on the one hand, and to isoperimetric inequalities in Geometry on the other. The book contains also an appendix, written by M. Gromov, which is an introduction to isoperimetric inequalities on riemannian manifolds. Only basic knowledge of Functional Analysis and Probability is expected of the reader. The book can be used (and was used by the authors) as a text for a first or second graduate course. The methods used here have been useful also in areas other than Functional Analysis (notably, Combinatorics).
Notes: Includes bibliographical references (p. [151]-156) and index.