Asymptotic Geometric Analysis, Part I

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

jún. 2015 · Mathematical Surveys and Monographs Bók 202 · American Mathematical Soc.

Rafbók

451

Síður

Einkunnir og umsagnir eru ekki staðfestar Nánar

Um þessa rafbók

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.

Gefa þessari rafbók einkunn.

Segðu okkur hvað þér finnst.

Upplýsingar um lestur

Snjallsímar og spjaldtölvur

Settu upp forritið Google Play Books fyrir Android og iPad/iPhone. Það samstillist sjálfkrafa við reikninginn þinn og gerir þér kleift að lesa með eða án nettengingar hvar sem þú ert.

Fartölvur og tölvur

Hægt er að hlusta á hljóðbækur sem keyptar eru í Google Play í vafranum í tölvunni.

Lesbretti og önnur tæki

Til að lesa af lesbrettum eins og Kobo-lesbrettum þarftu að hlaða niður skrá og flytja hana yfir í tækið þitt. Fylgdu nákvæmum leiðbeiningum hjálparmiðstöðvar til að flytja skrár yfir í studd lesbretti.

Tilkynna ólöglegt efni