Asymptotic Geometric Analysis, Part I

Shiri Artstein-Avidan · Apostolos Giannopoulos · Vitali D. Milman

juuni 2015 · Mathematical Surveys and Monographs 202. raamat · American Mathematical Soc.

E-raamat

451

lehekülge

Hinnangud ja arvustused pole kinnitatud. Lisateave

Teave selle e-raamatu kohta

The authors present the theory of asymptotic geometric analysis, a field which lies on the border between geometry and functional analysis. In this field, isometric problems that are typical for geometry in low dimensions are substituted by an "isomorphic" point of view, and an asymptotic approach (as dimension tends to infinity) is introduced. Geometry and analysis meet here in a non-trivial way. Basic examples of geometric inequalities in isomorphic form which are encountered in the book are the "isomorphic isoperimetric inequalities" which led to the discovery of the "concentration phenomenon", one of the most powerful tools of the theory, responsible for many counterintuitive results.

A central theme in this book is the interaction of randomness and pattern. At first glance, life in high dimension seems to mean the existence of multiple "possibilities", so one may expect an increase in the diversity and complexity as dimension increases. However, the concentration of measure and effects caused by convexity show that this diversity is compensated and order and patterns are created for arbitrary convex bodies in the mixture caused by high dimensionality.

The book is intended for graduate students and researchers who want to learn about this exciting subject. Among the topics covered in the book are convexity, concentration phenomena, covering numbers, Dvoretzky-type theorems, volume distribution in convex bodies, and more.

Hinnake seda e-raamatut

Andke meile teada, mida te arvate.

Lugemisteave

Nutitelefonid ja tahvelarvutid

Installige rakendus Google Play raamatud Androidile ja iPadile/iPhone'ile. See sünkroonitakse automaatselt teie kontoga ja see võimaldab teil asukohast olenemata lugeda nii võrgus kui ka võrguühenduseta.

Sülearvutid ja arvutid

Google Playst ostetud audioraamatuid saab kuulata arvuti veebibrauseris.

E-lugerid ja muud seadmed

E-tindi seadmetes (nt Kobo e-lugerid) lugemiseks peate faili alla laadima ja selle oma seadmesse üle kandma. Failide toetatud e-lugeritesse teisaldamiseks järgige üksikasjalikke abikeskuse juhiseid.

Ebaseaduslikust sisust teatamine