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Title
Random walks on infinite groups / Steven P. Lalley.
ISBN
9783031256325 (electronic bk.)
3031256328 (electronic bk.)
303125631X
9783031256318
Publication Details
Cham : Springer, 2023.
Language
English
Description
1 online resource.
Item Number
10.1007/978-3-031-25632-5 doi
Call Number
QA274.73
Dewey Decimal Classification
519.2/82
Summary
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.
Access Note
Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed May 22, 2023).
Series
Graduate texts in mathematics ; 297.
Available in Other Form
Print version: 9783031256318
1 First Steps
2 The Ergodic Theorem
3 Subadditivity and its Ramifications
4 The Carne-Varopoulos Inequality
5 Isoperimetric Inequalities and Amenability
6 Markov Chains and Harmonic Functions
7 Dirichlets Principle and the Recurrence Type Theorem
8 Martingales
9 Bounded Harmonic Functions
10 Entropy
11 Compact Group Actions and Boundaries
12 Poisson Boundaries
13 Hyperbolic Groups
14 Unbounded Harmonic Functions
15 Groups of Polynomial Growth
Appendix A: A 57-Minute Course in MeasureTheoretic Probability.
