Random Walks on Infinite Groups: 297 - Brossura

Lalley, Steven P.

Brossura

ISBN 10: 3031256344 ISBN 13: 9783031256349

Casa editrice: Springer Nature, 2024

Riassunto

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.

Su questo libro

Informazioni sull?autore

Steven 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.

Dalla quarta di copertina

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.

Dettagli dell'edizione

• Editore: Springer Nature
• Data di pubblicazione: 2024
• Lingua: Inglese
• ISBN 10: 3031256344
• ISBN 13: 9783031256349
• Rilegatura: Copertina flessibile
• Numero di pagine: 384
• Contatto del produttore: non disponibile
• Persona responsabile: CMN Printpool Inh. Mathis Neumann; https://www.also.com/ec/cms5/en_6000/6000/index.jsp; ; Friedrich-Karl-Str. 9; Hamburg; Germania