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Random Walks on Infinite Groups

2023-05-08 Mathematics
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Release : 2023-05-08
Genre : Mathematics
Kind : eBook
Book Rating : 328/5 ( reviews)

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Book Synopsis Random Walks on Infinite Groups by : Steven P. Lalley

Download or read book Random Walks on Infinite Groups written by Steven P. Lalley. This book was released on 2023-05-08. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Random Walks and Geometry

2008-08-22 Mathematics
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Release : 2008-08-22
Genre : Mathematics
Kind : eBook
Book Rating : 088/5 ( reviews)

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Book Synopsis Random Walks and Geometry by : Vadim Kaimanovich

Download or read book Random Walks and Geometry written by Vadim Kaimanovich. This book was released on 2008-08-22. Available in PDF, EPUB and Kindle. Book excerpt: Die jüngsten Entwicklungen zeigen, dass sich Wahrscheinlichkeitsverfahren zu einem sehr wirkungsvollen Werkzeug entwickelt haben, und das auf so unterschiedlichen Gebieten wie statistische Physik, dynamische Systeme, Riemann'sche Geometrie, Gruppentheorie, harmonische Analyse, Graphentheorie und Informatik.

Combinatorial and Computational Geometry

2005-08-08 Computers
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Release : 2005-08-08
Genre : Computers
Kind : eBook
Book Rating : 626/5 ( reviews)

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Book Synopsis Combinatorial and Computational Geometry by : Jacob E. Goodman

Download or read book Combinatorial and Computational Geometry written by Jacob E. Goodman. This book was released on 2005-08-08. Available in PDF, EPUB and Kindle. Book excerpt: This 2005 book deals with interest topics in Discrete and Algorithmic aspects of Geometry.

Random Walks on Infinite Graphs and Groups

2000-02-13 Mathematics
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Release : 2000-02-13
Genre : Mathematics
Kind : eBook
Book Rating : 923/5 ( reviews)

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Book Synopsis Random Walks on Infinite Graphs and Groups by : Wolfgang Woess

Download or read book Random Walks on Infinite Graphs and Groups written by Wolfgang Woess. This book was released on 2000-02-13. Available in PDF, EPUB and Kindle. Book excerpt: The main theme of this book is the interplay between the behaviour of a class of stochastic processes (random walks) and discrete structure theory. The author considers Markov chains whose state space is equipped with the structure of an infinite, locally finite graph, or as a particular case, of a finitely generated group. The transition probabilities are assumed to be adapted to the underlying structure in some way that must be specified precisely in each case. From the probabilistic viewpoint, the question is what impact the particular type of structure has on various aspects of the behaviour of the random walk. Vice-versa, random walks may also be seen as useful tools for classifying, or at least describing the structure of graphs and groups. Links with spectral theory and discrete potential theory are also discussed. This book will be essential reading for all researchers working in stochastic process and related topics.

Topics in Groups and Geometry

2022-01-01 Mathematics
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Release : 2022-01-01
Genre : Mathematics
Kind : eBook
Book Rating : 091/5 ( reviews)

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Book Synopsis Topics in Groups and Geometry by : Tullio Ceccherini-Silberstein

Download or read book Topics in Groups and Geometry written by Tullio Ceccherini-Silberstein. This book was released on 2022-01-01. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a detailed exposition of a wide range of topics in geometric group theory, inspired by Gromov’s pivotal work in the 1980s. It includes classical theorems on nilpotent groups and solvable groups, a fundamental study of the growth of groups, a detailed look at asymptotic cones, and a discussion of related subjects including filters and ultrafilters, dimension theory, hyperbolic geometry, amenability, the Burnside problem, and random walks on groups. The results are unified under the common theme of Gromov’s theorem, namely that finitely generated groups of polynomial growth are virtually nilpotent. This beautiful result gave birth to a fascinating new area of research which is still active today. The purpose of the book is to collect these naturally related results together in one place, most of which are scattered throughout the literature, some of them appearing here in book form for the first time. In this way, the connections between these topics are revealed, providing a pleasant introduction to geometric group theory based on ideas surrounding Gromov's theorem. The book will be of interest to mature undergraduate and graduate students in mathematics who are familiar with basic group theory and topology, and who wish to learn more about geometric, analytic, and probabilistic aspects of infinite groups.

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