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9783031256349: Random Walks on Infinite Groups: 297 (Graduate Texts in Mathematics)

Sinopsis

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.

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Acerca del autor

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.

De la contraportada

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.

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Steven P Lalley
Publicado por Springer Verlag Gmbh Mai 2024, 2024
ISBN 10: 3031256344 ISBN 13: 9783031256349
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Taschenbuch. Condición: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware Englisch. Nº de ref. del artículo: 9783031256349

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Steven P. Lalley
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Taschenbuch. Condición: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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 coursecovering 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. Nº de ref. del artículo: 9783031256349

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Lalley, Steven P.
ISBN 10: 3031256344 ISBN 13: 9783031256349
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Condición: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 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/non. Nº de ref. del artículo: 1658771023

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Steven P. Lalley
ISBN 10: 3031256344 ISBN 13: 9783031256349
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Taschenbuch. Condición: Neu. Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 384 pp. Englisch. Nº de ref. del artículo: 9783031256349

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Lalley, Steven P.
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Lalley, Steven P.
Publicado por Springer, 2024
ISBN 10: 3031256344 ISBN 13: 9783031256349
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