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OverviewThis 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. Full Product DetailsAuthor: Steven P. LalleyPublisher: Springer International Publishing AG Imprint: Springer International Publishing AG Edition: 1st ed. 2023 Volume: 297 Weight: 0.810kg ISBN: 9783031256318ISBN 10: 303125631 Pages: 369 Publication Date: 09 May 2023 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: Manufactured on demand We will order this item for you from a manufactured on demand supplier. Table of ContentsReviewsAuthor InformationSteven P. Lalley is professor Emeritus at the Department of Statistics at the University of Chicago. His research includes probability and random processes, in particular: stochastic interacting systems, random walk, percolation, branching processes, combinatorial probability, ergodic theory, and connections between probability and geometry. Tab Content 6Author Website:Countries AvailableAll regions |