Harmonic functions and random walks on groups /
Yadin, Ariel
Harmonic functions and random walks on groups / Ariel Yadin - United Kingdom Cambridge University Press 2024 - 381 p.
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.
9781009123181
Harmonic functions
Random walk entropy
Choquet–Deny Theorem
Milnor–Wolf Theorem
Gromov's Theorem
Polynomial growth groups
515.7 YAD-A
Harmonic functions and random walks on groups / Ariel Yadin - United Kingdom Cambridge University Press 2024 - 381 p.
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.
9781009123181
Harmonic functions
Random walk entropy
Choquet–Deny Theorem
Milnor–Wolf Theorem
Gromov's Theorem
Polynomial growth groups
515.7 YAD-A