Groups, Graphs and Random Walks
Published on 29. June 2017
Book
Paperback/Softback
536 pages
978-1-316-60440-3 (ISBN)
Description
An accessible and panoramic account of the theory of random walks on groups and graphs, stressing the strong connections of the theory with other branches of mathematics, including geometric and combinatorial group theory, potential analysis, and theoretical computer science. This volume brings together original surveys and research-expository papers from renowned and leading experts, many of whom spoke at the workshop 'Groups, Graphs and Random Walks' celebrating the sixtieth birthday of Wolfgang Woess in Cortona, Italy. Topics include: growth and amenability of groups; Schroedinger operators and symbolic dynamics; ergodic theorems; Thompson's group F; Poisson boundaries; probability theory on buildings and groups of Lie type; structure trees for edge cuts in networks; and mathematical crystallography. In what is currently a fast-growing area of mathematics, this book provides an up-to-date and valuable reference for both researchers and graduate students, from which future research activities will undoubtedly stem.
Reviews / Votes
'All parts are carefully presented, often tending to be self-contained and well documented ... historical developments as well as significant fields of application of the theory are described for the enlightenment of the reader.' Jean-Guillaume Eon, Actas Crystallographica, Section AMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Product notice
Paperback (trade)
Illustrations
Worked examples or Exercises; 32 Halftones, black and white; 38 Line drawings, black and white
Dimensions
Height: 229 mm
Width: 152 mm
Thickness: 31 mm
Weight
864 gr
ISBN-13
978-1-316-60440-3 (9781316604403)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Tullio Ceccherini-Silberstein
Groups, Graphs and Random Walks
E-Book
06/2017
Cambridge University Press
€66.49
Available for download
Tullio Ceccherini-Silberstein | Maura Salvatori | Ecaterina Sava-Huss
Groups, Graphs and Random Walks
E-Book
06/2017
Cambridge University Press
€79.99
Available for download
Persons
Tullio Ceccherini-Silberstein is a professor in the Department of Engineering at Universit... del Sannio (Benevento), Italy. Maura Salvatori is an associate professor in the Department of Mathematics at Universit... degli Studi di Milano, Italy. Ecaterina Sava-Huss is a visiting assistant professor in the Department of Mathematics at Cornell University, New York.
Content
1. Growth of groups and wreath products Laurent Bartholdi; 2. Random walks on some countable groups Alexander Bendikov and Laurent Saloff-Coste; 3. The cost of distinguishing graphs Debra Boutin and Wilfried Imrich; 4. A construction of the measurable Poisson boundary - from discrete to continuous groups Sara Brofferio; 5. Structure trees, networks and almost invariant sets Martin J. Dunwoody; 6. Amenability of trees Behrang Forghani and Keivan Mallahi-Karai; 7. Group-walk random groups Agelos Georgakopoulos; 8. Ends of branching random walks on planar hyperbolic Cayley graphs Lorenz A. Gilch and Sebastian Mueller; 9. Amenability and ergodic properties of topological groups - from Bogolyubov onwards Rostislav Grigorchuk and Pierre de la Harpe; 10. Schreier graphs of Grigorchuk's group and a subshift associated to a non-primitive substitution Rostislav Grigorchuk, Daniel Lenz and Tatiana Nagnibeda; 11. Thompson's group F is not Liouville Vadim A. Kaimanovich; 12. A proof of the subadditive ergodic theorem Anders Karlsson; 13. Boundaries of Zn-free groups Andrei Malyutin, Tatiana Nagnibeda and Denis Serbin; 14. Buildings, groups of Lie type, and random walks James Parkinson; 15. On some random walks driven by spread-out measures Laurent Saloff-Coste and Tianyi Zheng; 16. Topics in mathematical crystallography Toshikazu Sunada.