ENGLISH

Harmonic Functions and Random Walks on Groups

By Ariel Yadin

Book information

Publisher
Cambridge University Press
Year
2024
ISBN
9781009123181, 9781009128391
DOI
10.1017/9781009128391
Language
english
Format
PDF
Filesize
9 MB (9188363 bytes)
Series
Cambridge Studies in Advanced Mathematics 213
Edition
1
Pages
381\403
Orientation
yes
Paginated
no
Scanned
portrait
Time added
2024-05-20 13:03:00
Gromov's TheoremGroupsHarmonic FunctionsHeat KernelMarkov ChainsMartingalesMilnor-Wolf TheoremNetworks

Description

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.

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