11 edition of **Random walks on infinite graphs and groups** found in the catalog.

- 337 Want to read
- 23 Currently reading

Published
**2000**
by Cambridge University Press in Cambridge, New York
.

Written in English

- Random walks (Mathematics),
- Graph theory.,
- Infinite groups.

**Edition Notes**

Includes bibliographical references (p. 316-330) and index.

Statement | Wolfgang Woess. |

Series | Cambridge tracts in mathematics ;, 138 |

Classifications | |
---|---|

LC Classifications | QA274.73 .W64 2000 |

The Physical Object | |

Pagination | xi, 334 p. : |

Number of Pages | 334 |

ID Numbers | |

Open Library | OL40039M |

ISBN 10 | 0521552923 |

LC Control Number | 99030069 |

Random Walks on Infinite Graphs and Groups, Paperback by Woess, Wolfgang, ISBN , ISBN , Brand New, Free shipping in the US The main theme of this book is the interplay between random walks and discrete structure theory. For infinite graphs, a study of the heat kernel allows to solve the type problem—a problem of deciding whether the random walk is recurrent or transient. This book starts with elementary properties of the eigenvalues on finite graphs, continues with their estimates and applications, and concludes with heat kernel estimates on infinite graphs.

RANDOM WALKS ON INFINITE GRAPHS AND GROUPS. By. Abstract. The simple random walk on the integers is one of the simplest random processes that one can imagine. It generalizes to any finitely generated group Γ equipped book reviews with a finite set S of generators. If Xn ∈ Γ denotes the position at time n, then Xn+1 = Xnξn+1, where ξn. Coulhon T., Random walks and geometry on infinite graphs, in: “Lecture notes on analysis on metric spaces”, ed. Luigi Ambrosio, Francesco Serra Cassano, Scuola Normale Superiore di Pisa, 5–

@ARTICLE{Woess94randomwalks, author = {Wolfgang Woess}, title = {Random walks on infinite graphs and groups - a survey on selected topics}, journal = {Bull. London Math. Soc}, year = {}, volume = {26}, pages = {}} Share. OpenURL. Abstract. 2. Basic definitions and preliminaries 3 A. Adaptedness to the graph structure 4 B. Reversible. random walk on the graph. A random walk is a ﬁnite Markov chain that is time-reversible (see below). In fact, there is not much diﬀerence between the theory of random walks on graphs and the theory of ﬁnite Markov chains; every Markov chain can be viewed as random walk on a directed graph, if we allow weighted edges.

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Vice-versa, random walks may also be seen as useful tools for classifying, or at least describing the structure of graphs and groups. This book will be essential reading for all researchers working in stochastic process and related by: 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 by: This eminent work focuses on the interplay between the behavior of random walks and discrete structure theory.

Wolfgang Woess considers Markov chains whose state space is equipped with the structure of an infinite, locally-finite graph, or of a finitely generated group. Random Walks on Infinite Graphs and Groups - by Wolfgang Woess February Email your librarian or administrator to recommend adding this book to your organisation's collection.

Random Walks on Infinite Graphs and Groups. Wolfgang Woess; Online ISBN: The main Random walks on infinite graphs and groups book 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.5/5(1). Growth, isoperimetric inequalities, and the asymptotic type of random walk The asymptotic type of random walks on amenable groups Simple random walks on the Sierpinski graphs Local limit theorems on free products Intermezzo: Cartesian products Free groups and homogeneous trees Chapter IV.

RANDOM WALKS ON INFINITE GRAPHS AND GROUPS (Cambridge Tracts in Mathematics ) (US$), isbn (Cambridge University Press, ).

The simple random walk on the integers is one of the simplest random processes that one can imagine. It generalizes to any nitely generated group Γ equipped.

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. Random walks on graphs 7 D. Trees 9 E. Random walks on finitely generated groups 10 F. Locally finite graphs and topological groups 12 2. Recurrence and transience of infinite networks 14 A.

Reversible Markov chains 14 B. Flows, capacity, and Nash-Williams' criterion 18 C. Comparison with non-reversible Markov chains 23 3.

Applications to. RANDOM WALKS ON INFINITE GRAPHS AND GROUPS 3 random walks on integer lattices (besides those covered by Spitze [r o] r by Barber and Ninham [15]) was abandoned in view of the length of the material accumulated already.

To give an idea, we mention here a few references, chosen 'at random': Schinzel [] Keste, n [] Erdo, s and Revesz [ The main theme of this book is the interplay between the behaviour of a class of stochastic processes (random walks) and discrete structure theory.

Besides a detailed exposition of probabilistic and structure theoretic aspects, links with spectral theory and discrete potential theory are also discussed. This introduction to random walks on infinite graphs gives particular emphasis to graphs with polynomial volume growth.

It offers an overview of analytic methods, starting with the connection between random walks and electrical resistance, and then proceeding to study the use of isoperimetric and Poincaré inequalities.

Reversible Markov Chains and Random Walks on Graphs (by Aldous and Fill: unfinished monograph) In response to many requests, the material posted as separate chapters since the s (see bottom of page) has been recompiled as a single PDF document which nowadays is searchable.

CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): The simple random walk on the integers is one of the simplest random processes that one can imagine. It generalizes to any finitely generated group Γ equipped book reviews with a finite set S of generators.

If Xn ∈ Γ denotes the position at time n, then Xn+1 = Xnξn+1, where ξn is chosen uniformly at random in S. Leading experts' results from group-theory, probability, ergodic theory, and analysis: diverse spectrum of high level research on the topic of random walks on infinite graphs.

Diverse spectrum of sub-fields; Up-to-date overviews of random walks, graphs, spectra under different perspectives; see more benefits.

"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.

Book Review in Bull. Amer. Math. Soc. “Random walks on infinite graphs and groups” by W. Woess Article (PDF Available) in Bulletin of the American Mathematical Society January. Random Walks in Random Environments. Mixing times for some random regular graphs; Randomizing infinite trees; Bias and speed; Finite random trees; Randomly-weighted random graphs; Random environments in d d dimensions; Notes on Chapter 13; 14 Interacting Particles on Finite Graphs (March Percolation on Transitive Graphs The Mass-Transport Principle and Percolation Infinite Electrical Networks and Dirichlet Functions Uniform Spanning Forests Minimal Spanning Forests Limit Theorems for Galton-Watson Processes Escape Rate of Random Walks and Embeddings Random Walks on Groups and Poisson Boundaries Hausdorff Dimension.

Random Walks on Infinite Graphs and Groups. publ. ed.) (Cambridge Tracts in Mathematics). Cambridge, UK: Cambridge University by:. In mathematics, a random walk is a mathematical object, known as a stochastic or random process, that describes a path that consists of a succession of random steps on some mathematical space such as the integers.

An elementary example of a random walk is the random walk on the integer number line, which starts at 0 and at each step moves +1 or −1 with equal probability.Abstract.

We introduce two new techniques to the analysis on fractals. One is based on the presentation of the fractal as the boundary of a countable Gromov hyperbolic graph, whereas the other one consists in taking all possible “backward” extensions of the above hyperbolic graph and considering them as the classes of a discrete equivalence relation on an appropriate compact space.Continuous-time random walk 12 Other lattices 14 Other walks 16 Simple random walk on a graph Generating functions and loop measures Loop soup This project embarked with an idea of writing a book on the simple, nearest neighbor random walk.

Symmetric, ﬁnite range random walks gradually became the.