Harmonic functions and random walks on groups / Ariel Yadin.

Format:

Book

Author/Creator:

Yadin, Ariel, author.

Series:

Cambridge studies in advanced mathematics ; 213.

Cambridge studies in advanced mathematics ; 213

Language:

English

Subjects (All):

Harmonic functions.

Physical Description:

1 online resource (xix, 381 pages) : digital, PDF file(s).

Edition:

First edition.

Place of Publication:

Cambridge : Cambridge University Press, 2024.

Summary:

Research in recent years has highlighted the deep connections between the algebraic, geometric, and analytic structures of a discrete group. New methods and ideas have resulted in an exciting field, with many opportunities for new researchers. This book is an introduction to the area from a modern vantage point. It incorporates the main basics, such as Kesten's amenability criterion, Coulhon and Saloff-Coste inequality, random walk entropy and bounded harmonic functions, the Choquet-Deny Theorem, the Milnor-Wolf Theorem, and a complete proof of Gromov's Theorem on polynomial growth groups. The book is especially appropriate for young researchers, and those new to the field, accessible even to graduate students. An abundance of examples, exercises, and solutions encourage self-reflection and the internalization of the concepts introduced. The author also points to open problems and possibilities for further research.

Notes:

Title from publisher's bibliographic system (viewed on 16 May 2024).

Includes bibliographical references and index.

ISBN:

9781009546577

1009546570

9781009128391

1009128396