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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.

Groups, Graphs and Random Walks

2017-06-29 Mathematics
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Release : 2017-06-29
Genre : Mathematics
Kind : eBook
Book Rating : 784/5 ( reviews)

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Book Synopsis Groups, Graphs and Random Walks by : Tullio Ceccherini-Silberstein

Download or read book Groups, Graphs and Random Walks written by Tullio Ceccherini-Silberstein. This book was released on 2017-06-29. Available in PDF, EPUB and Kindle. Book excerpt: 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; Schrödinger 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.

Groups, Graphs and Random Walks

2017-06-29 Mathematics
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Release : 2017-06-29
Genre : Mathematics
Kind : eBook
Book Rating : 403/5 ( reviews)

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Book Synopsis Groups, Graphs and Random Walks by : Tullio Ceccherini-Silberstein

Download or read book Groups, Graphs and Random Walks written by Tullio Ceccherini-Silberstein. This book was released on 2017-06-29. Available in PDF, EPUB and Kindle. Book excerpt: An up-to-date, panoramic account of the theory of random walks on groups and graphs, outlining connections with various mathematical fields.

Probability on Trees and Networks

2017-01-20 Mathematics
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Release : 2017-01-20
Genre : Mathematics
Kind : eBook
Book Rating : 335/5 ( reviews)

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Book Synopsis Probability on Trees and Networks by : Russell Lyons

Download or read book Probability on Trees and Networks written by Russell Lyons. This book was released on 2017-01-20. Available in PDF, EPUB and Kindle. Book excerpt: Starting around the late 1950s, several research communities began relating the geometry of graphs to stochastic processes on these graphs. This book, twenty years in the making, ties together research in the field, encompassing work on percolation, isoperimetric inequalities, eigenvalues, transition probabilities, and random walks. Written by two leading researchers, the text emphasizes intuition, while giving complete proofs and more than 850 exercises. Many recent developments, in which the authors have played a leading role, are discussed, including percolation on trees and Cayley graphs, uniform spanning forests, the mass-transport technique, and connections on random walks on graphs to embedding in Hilbert space. This state-of-the-art account of probability on networks will be indispensable for graduate students and researchers alike.

Random Walks and Electric Networks

1984-12-31 Electric network topology
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Release : 1984-12-31
Genre : Electric network topology
Kind : eBook
Book Rating : 220/5 ( reviews)

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Book Synopsis Random Walks and Electric Networks by : Peter G. Doyle

Download or read book Random Walks and Electric Networks written by Peter G. Doyle. This book was released on 1984-12-31. Available in PDF, EPUB and Kindle. Book excerpt: Probability theory, like much of mathematics, is indebted to physics as a source of problems and intuition for solving these problems. Unfortunately, the level of abstraction of current mathematics often makes it difficult for anyone but an expert to appreciate this fact. Random Walks and electric networks looks at the interplay of physics and mathematics in terms of an example—the relation between elementary electric network theory and random walks —where the mathematics involved is at the college level.

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