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Springer Random Walks on Infinite Groups: Graduate Texts in Mathematics 297

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Description

This graduate-level textbook by Springer presents the foundational theory of random walks on infinite, finitely generated groups, integrating essential measure-theoretic probability concepts. The work explores how structural properties of groups-particularly amenability and nonamenability-shape the qualitative behaviour of symmetric random walks, including transience, recurrence, speed, entropy, and the existence of bounded harmonic functions. Designed for beginning graduate-level courses and independent study, this comprehensive volume serves advanced undergraduate and graduate students seeking rigorous grounding in the intersection of group theory and stochastic processes. The text bridges abstract algebra and probability theory through carefully developed arguments and systematic exposition of random walk dynamics on infinite group structures.

Key Features

Covers random walks on infinite, finitely generated groups with foundational theory and measure-theoretic probability background.

Examines how group amenability and nonamenability properties affect transience, recurrence, and speed of symmetric random walks.

Analyses entropy and bounded harmonic functions on groups using random walk methodology.

Suitable as a textbook for graduate-level courses in probability, group theory, and geometric group theory.

Comprehensive treatment integrates structural group properties with qualitative random walk behaviour.

Product Specifications

Format
paperback
Domain
Amazon UK
Release Date
10 May 2024
Listed Since
11 May 2024

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