Random Walks on Infinite Graphs and Groups

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Publisher : Cambridge University Press
ISBN 13 : 0521552923
Total Pages : 350 pages
Book Rating : 4.5/5 (215 download)

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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 and published by Cambridge University Press. This book was released on 2000-02-13 with total page 350 pages. 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

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Publisher :
ISBN 13 : 9781316818862
Total Pages : pages
Book Rating : 4.8/5 (188 download)

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Book Synopsis Groups, Graphs, and Random Walks by : TULLIO CECCHERINI-SILBERSTEIN;MAURA SALVATORI;ECAT.

Download or read book Groups, Graphs, and Random Walks written by TULLIO CECCHERINI-SILBERSTEIN;MAURA SALVATORI;ECAT. and published by . This book was released on with total page pages. 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.

Random Graph Dynamics

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Publisher : Cambridge University Press
ISBN 13 : 1139460889
Total Pages : 203 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Random Graph Dynamics by : Rick Durrett

Download or read book Random Graph Dynamics written by Rick Durrett and published by Cambridge University Press. This book was released on 2010-05-31 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of random graphs began in the late 1950s in several papers by Erdos and Renyi. In the late twentieth century, the notion of six degrees of separation, meaning that any two people on the planet can be connected by a short chain of people who know each other, inspired Strogatz and Watts to define the small world random graph in which each site is connected to k close neighbors, but also has long-range connections. At a similar time, it was observed in human social and sexual networks and on the Internet that the number of neighbors of an individual or computer has a power law distribution. This inspired Barabasi and Albert to define the preferential attachment model, which has these properties. These two papers have led to an explosion of research. The purpose of this book is to use a wide variety of mathematical argument to obtain insights into the properties of these graphs. A unique feature is the interest in the dynamics of process taking place on the graph in addition to their geometric properties, such as connectedness and diameter.

Groups, Graphs and Random Walks

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Publisher : Cambridge University Press
ISBN 13 : 1316817784
Total Pages : 539 pages
Book Rating : 4.3/5 (168 download)

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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 and published by Cambridge University Press. This book was released on 2017-06-29 with total page 539 pages. 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.

Probability on Trees and Networks

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Publisher : Cambridge University Press
ISBN 13 : 1316785335
Total Pages : 1106 pages
Book Rating : 4.3/5 (167 download)

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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 and published by Cambridge University Press. This book was released on 2017-01-20 with total page 1106 pages. 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.

Handbook of Dynamical Systems

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Publisher : Gulf Professional Publishing
ISBN 13 : 0080532845
Total Pages : 1099 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Handbook of Dynamical Systems by : B. Fiedler

Download or read book Handbook of Dynamical Systems written by B. Fiedler and published by Gulf Professional Publishing. This book was released on 2002-02-21 with total page 1099 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook is volume II in a series collecting mathematical state-of-the-art surveys in the field of dynamical systems. Much of this field has developed from interactions with other areas of science, and this volume shows how concepts of dynamical systems further the understanding of mathematical issues that arise in applications. Although modeling issues are addressed, the central theme is the mathematically rigorous investigation of the resulting differential equations and their dynamic behavior. However, the authors and editors have made an effort to ensure readability on a non-technical level for mathematicians from other fields and for other scientists and engineers. The eighteen surveys collected here do not aspire to encyclopedic completeness, but present selected paradigms. The surveys are grouped into those emphasizing finite-dimensional methods, numerics, topological methods, and partial differential equations. Application areas include the dynamics of neural networks, fluid flows, nonlinear optics, and many others. While the survey articles can be read independently, they deeply share recurrent themes from dynamical systems. Attractors, bifurcations, center manifolds, dimension reduction, ergodicity, homoclinicity, hyperbolicity, invariant and inertial manifolds, normal forms, recurrence, shift dynamics, stability, to namejust a few, are ubiquitous dynamical concepts throughout the articles.

Probability on Graphs

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Publisher : Cambridge University Press
ISBN 13 : 1108542999
Total Pages : 279 pages
Book Rating : 4.1/5 (85 download)

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Book Synopsis Probability on Graphs by : Geoffrey Grimmett

Download or read book Probability on Graphs written by Geoffrey Grimmett and published by Cambridge University Press. This book was released on 2018-01-25 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to some of the principal models in the theory of disordered systems leads the reader through the basics, to the very edge of contemporary research, with the minimum of technical fuss. Topics covered include random walk, percolation, self-avoiding walk, interacting particle systems, uniform spanning tree, random graphs, as well as the Ising, Potts, and random-cluster models for ferromagnetism, and the Lorentz model for motion in a random medium. This new edition features accounts of major recent progress, including the exact value of the connective constant of the hexagonal lattice, and the critical point of the random-cluster model on the square lattice. The choice of topics is strongly motivated by modern applications, and focuses on areas that merit further research. Accessible to a wide audience of mathematicians and physicists, this book can be used as a graduate course text. Each chapter ends with a range of exercises.

Random Walks and Electric Networks

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Publisher : American Mathematical Soc.
ISBN 13 : 1614440220
Total Pages : 159 pages
Book Rating : 4.6/5 (144 download)

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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 and published by American Mathematical Soc.. This book was released on 1984-12-31 with total page 159 pages. 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.

Random Walks and Heat Kernels on Graphs

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Publisher : Cambridge University Press
ISBN 13 : 1107674425
Total Pages : 239 pages
Book Rating : 4.1/5 (76 download)

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Book Synopsis Random Walks and Heat Kernels on Graphs by : M. T. Barlow

Download or read book Random Walks and Heat Kernels on Graphs written by M. T. Barlow and published by Cambridge University Press. This book was released on 2017-02-23 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: Useful but hard-to-find results enrich this introduction to the analytic study of random walks on infinite graphs.

Random walks on infinite graphs and groups

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Publisher :
ISBN 13 :
Total Pages : 65 pages
Book Rating : 4.:/5 (257 download)

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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 and published by . This book was released on 1991 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Random Walk

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Publisher :
ISBN 13 : 9780511750113
Total Pages : 378 pages
Book Rating : 4.7/5 (51 download)

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Book Synopsis Random Walk by : Gregory F. Lawler

Download or read book Random Walk written by Gregory F. Lawler and published by . This book was released on 2014-05-14 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: An advanced treatment of random walks written for students and researchers in probability and related fields.

Equidistribution and Counting Under Equilibrium States in Negative Curvature and Trees

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Publisher : Birkhäuser
ISBN 13 : 9783030183141
Total Pages : 413 pages
Book Rating : 4.1/5 (831 download)

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Book Synopsis Equidistribution and Counting Under Equilibrium States in Negative Curvature and Trees by : Anne Broise-Alamichel

Download or read book Equidistribution and Counting Under Equilibrium States in Negative Curvature and Trees written by Anne Broise-Alamichel and published by Birkhäuser. This book was released on 2020-01-02 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a complete exposition of equidistribution and counting problems weighted by a potential function of common perpendicular geodesics in negatively curved manifolds and simplicial trees. Avoiding any compactness assumptions, the authors extend the theory of Patterson-Sullivan, Bowen-Margulis and Oh-Shah (skinning) measures to CAT(-1) spaces with potentials. The work presents a proof for the equidistribution of equidistant hypersurfaces to Gibbs measures, and the equidistribution of common perpendicular arcs between, for instance, closed geodesics. Using tools from ergodic theory (including coding by topological Markov shifts, and an appendix by Buzzi that relates weak Gibbs measures and equilibrium states for them), the authors further prove the variational principle and rate of mixing for the geodesic flow on metric and simplicial trees—again without the need for any compactness or torsionfree assumptions. In a series of applications, using the Bruhat-Tits trees over non-Archimedean local fields, the authors subsequently prove further important results: the Mertens formula and the equidistribution of Farey fractions in function fields, the equidistribution of quadratic irrationals over function fields in their completions, and asymptotic counting results of the representations by quadratic norm forms. One of the book's main benefits is that the authors provide explicit error terms throughout. Given its scope, it will be of interest to graduate students and researchers in a wide range of fields, for instance ergodic theory, dynamical systems, geometric group theory, discrete subgroups of locally compact groups, and the arithmetic of function fields.

Random Walks and Geometry

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Publisher : Walter de Gruyter
ISBN 13 : 3110198088
Total Pages : 545 pages
Book Rating : 4.1/5 (11 download)

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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 and published by Walter de Gruyter. This book was released on 2008-08-22 with total page 545 pages. 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.

Two-Dimensional Random Walk

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Publisher : Cambridge University Press
ISBN 13 : 1108472451
Total Pages : 224 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis Two-Dimensional Random Walk by : Serguei Popov

Download or read book Two-Dimensional Random Walk written by Serguei Popov and published by Cambridge University Press. This book was released on 2021-03-18 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: A visual, intuitive introduction in the form of a tour with side-quests, using direct probabilistic insight rather than technical tools.

Probability on Discrete Structures

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Publisher : Springer Science & Business Media
ISBN 13 : 3662094444
Total Pages : 358 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Probability on Discrete Structures by : Harry Kesten

Download or read book Probability on Discrete Structures written by Harry Kesten and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most probability problems involve random variables indexed by space and/or time. These problems almost always have a version in which space and/or time are taken to be discrete. This volume deals with areas in which the discrete version is more natural than the continuous one, perhaps even the only one than can be formulated without complicated constructions and machinery. The 5 papers of this volume discuss problems in which there has been significant progress in the last few years; they are motivated by, or have been developed in parallel with, statistical physics. They include questions about asymptotic shape for stochastic growth models and for random clusters; existence, location and properties of phase transitions; speed of convergence to equilibrium in Markov chains, and in particular for Markov chains based on models with a phase transition; cut-off phenomena for random walks. The articles can be read independently of each other. Their unifying theme is that of models built on discrete spaces or graphs. Such models are often easy to formulate. Correspondingly, the book requires comparatively little previous knowledge of the machinery of probability.

Introduction to Random Graphs

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Publisher : Cambridge University Press
ISBN 13 : 1107118506
Total Pages : 483 pages
Book Rating : 4.1/5 (71 download)

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Book Synopsis Introduction to Random Graphs by : Alan Frieze

Download or read book Introduction to Random Graphs written by Alan Frieze and published by Cambridge University Press. This book was released on 2016 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: The text covers random graphs from the basic to the advanced, including numerous exercises and recommendations for further reading.

Combinatorics, Paul Erdős is Eighty

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Publisher :
ISBN 13 :
Total Pages : 528 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Combinatorics, Paul Erdős is Eighty by : Paul Erdős

Download or read book Combinatorics, Paul Erdős is Eighty written by Paul Erdős and published by . This book was released on 1993 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: