Random Walks on Infinite Groups
Buch in deiner Nähe kaufen
Beschreibung
This text presents the basic theory of random walks on infinite, finitely generated groups, along with certain background material in measure-theoretic probability. The main objective is to show how structural features of a group, such as amenability/nonamenability, affect qualitative aspects of symmetric random walks on the group, such as transience/recurrence, speed, entropy, and existence or nonexistence of nonconstant, bounded harmonic functions. The book will be suitable as a textbook for beginning graduate-level courses or independent study by graduate students and advanced undergraduate students in mathematics with a solid grounding in measure theory and a basic familiarity with the elements of group theory. The first seven chapters could also be used as the basis for a short course covering the main results regarding transience/recurrence, decay of return probabilities, and speed. The book has been organized and written so as to be accessible not only to students in probability theory, but also to students whose primary interests are in geometry, ergodic theory, or geometric group theory.
This text presents the basic theory of random walks on infinite, finitely generated groups, along with certain background material in measure-theoretic probability. The main objective is to show how structural features of a group, such as amenability/nonamenability, affect qualitative aspects of symmetric random walks on the group, such as transience/recurrence, speed, entropy, and existence or nonexistence of nonconstant, bounded harmonic functions. The book will be suitable as a textbook for beginning graduate-level courses or independent study by graduate students and advanced undergraduate students in mathematics with a solid grounding in measure theory and a basic familiarity with the elements of group theory. The first seven chapters could also be used as the basis for a short course covering the main results regarding transience/recurrence, decay of return probabilities, and speed. The book has been organized and written so as to be accessible not only to students in probability theory, but also to students whose primary interests are in geometry, ergodic theory, or geometric group theory.
First textbook devoted solely to random walks on infinite, nonabelian groups Integrated treatment of measure-theoretic probability and random walk theory First textbook to treat Kleiner’s approach to Gromov’s classification theorem for groups of polynomial growth
Autor*in
Steven P. Lalley
Themen in »Random Walks on Infinite Groups«
Random walk Random walk textbook Random walk on finitely generated group Poisson boundaries of random walks Carne-Varoploulos inequality Isoperimetric inequalities Amenable groups Dirichlet's Principle Markov chains and harmonic functions Bounded harmonic functions Unbounded harmonic functions Groups of polynomial growth
Stimmen zu »Random Walks on Infinite Groups«
“The book is written clearly and the chapters are neatly arranged for easy reading. The book would be interesting to students/researchers involved in understanding and developing the interrelation between geometric/structural group theory and probability/random walks on groups.” (C. R. E. Raja, zbMATH 1555.60005, 2025)
“This book is about symmetric random walks on finitely generated infinite groups and consists of fifteen chapters followed by an appendix on measure and probability theories. It also offers good accounts on the theories of Markov chains valued in countable spaces and discrete-time martingales.” (Nizar Demni, Mathematical Reviews, May 8, 2024)
()