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OverviewFull Product DetailsAuthor: Ariel Yadin (Ben-Gurion University of the Negev, Israel)Publisher: Cambridge University Press Imprint: Cambridge University Press ISBN: 9781009123181ISBN 10: 1009123181 Pages: 398 Publication Date: 23 May 2024 Audience: College/higher education , Postgraduate, Research & Scholarly Format: Hardback Publisher's Status: Forthcoming Availability: Not yet available, will be POD  This item is yet to be released. You can pre-order this item and we will dispatch it to you upon it's release. This is a print on demand item which is still yet to be released. Table of ContentsPart I. Tools and Theory: 1. Background; 2. Martingales; 3. Markov chains; 4. Networks and discrete analysis; Part II. Results and Applications: 5. Growth, dimension, and heat kernel; 6. Bounded harmonic functions; 7. Choquet–Deny groups; 8. The Milnor–Wolf theorem; 9. Gromov's theorem; Appendices: A. Hilbert space background; B. Entropy; C. Coupling and total variation; References; Index.Reviews'This is a wonderful introduction to random walks and harmonic functions on finitely generated groups. The focus is the characterization of Choquet-Deny groups. The text offers a balanced treatment of well-chosen topics involving probabilistic and algebraic arguments presented with accuracy and care. The rich list of exercises with solutions will certainly help and entertain the reader.' Laurent Saloff-Coste, Cornell University 'Written by a leading expert in the field, this book explores the fundamental results of this captivating area at the boundary of probability and geometric group theory—an essential read for aspiring young researchers.' Hugo Duminil-Copin, Institut des Hautes Études Scientifiques and Université de Genève 'This voluminous book is a substantial contribution to the state of the art of random walk theory, which has evolved enormously in the last decades. A broad initial part on the basics is guided by numerous exercises. The core chapters are on the relation between harmonic functions for random walks and the structure of the underlying groups, in particular growth. The final highlight is a modern exposition of Gromov's theorem on polynomial growth and its strong interplay with the topics of the book's title.' Wolfgang Woess, Technische Universität Graz Author InformationAriel Yadin is Professor in the Department of Mathematics at Ben-Gurion University of the Negev. His research is focused on the interplay between random walks and the geometry of groups. He has taught a variety of courses on the subject, and has been part of a new wave of investigation into the structure of spaces of unbounded harmonic functions on groups. Tab Content 6Author Website:Countries AvailableAll regions |
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