Random Walks On Infinite Graphs And Groups
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Random Walks On Infinite Graphs And Groups
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Author : Wolfgang Woess
language : en
Publisher: Cambridge University Press
Release Date : 2000-02-13
Random Walks On Infinite Graphs And Groups written by Wolfgang Woess and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-02-13 with Mathematics categories.
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.
Random Walks On Infinite Graphs And Groups
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Author : Wolfgang Woess
language : en
Publisher:
Release Date : 1991
Random Walks On Infinite Graphs And Groups written by Wolfgang Woess and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with categories.
Random Walks Boundaries And Spectra
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Author : Daniel Lenz
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-16
Random Walks Boundaries And Spectra written by Daniel Lenz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-16 with Mathematics categories.
These proceedings represent the current state of research on the topics 'boundary theory' and 'spectral and probability theory' of random walks on infinite graphs. They are the result of the two workshops held in Styria (Graz and St. Kathrein am Offenegg, Austria) between June 29th and July 5th, 2009. Many of the participants joined both meetings. Even though the perspectives range from very different fields of mathematics, they all contribute with important results to the same wonderful topic from structure theory, which, by extending a quotation of Laurent Saloff-Coste, could be described by 'exploration of groups by random processes'.
Random Walks On Infinite Groups
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Author : Steven P. Lalley
language : en
Publisher: Springer Nature
Release Date : 2023-05-08
Random Walks On Infinite Groups written by Steven P. Lalley and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-08 with Mathematics categories.
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 Discrete Potential Theory
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Author : M. Picardello
language : en
Publisher: Cambridge University Press
Release Date : 1999-11-18
Random Walks And Discrete Potential Theory written by M. Picardello and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-11-18 with Mathematics categories.
Comprehensive and interdisciplinary text covering the interplay between random walks and structure theory.
Groups Graphs And Random Walks
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Author : Tullio Ceccherini-Silberstein
language : en
Publisher: Cambridge University Press
Release Date : 2017-06-29
Groups Graphs And Random Walks written by Tullio Ceccherini-Silberstein and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-29 with Mathematics categories.
An up-to-date, panoramic account of the theory of random walks on groups and graphs, outlining connections with various mathematical fields.
Probability On Graphs
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Author : Geoffrey Grimmett
language : en
Publisher: Cambridge University Press
Release Date : 2010-06-24
Probability On Graphs written by Geoffrey Grimmett and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-24 with Mathematics categories.
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. Schramm–Löwner evolutions (SLE) arise in various contexts. The choice of topics is strongly motivated by modern applications and focuses on areas that merit further research. Special features include a simple account of Smirnov's proof of Cardy's formula for critical percolation, and a fairly full account of the theory of influence and sharp-thresholds. 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 Geometry
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Author : Vadim Kaimanovich
language : en
Publisher: Walter de Gruyter
Release Date : 2008-08-22
Random Walks And Geometry written by Vadim Kaimanovich and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-22 with Mathematics categories.
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.
Random Graph Dynamics
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Author : Rick Durrett
language : en
Publisher: Cambridge University Press
Release Date : 2010-05-31
Random Graph Dynamics written by Rick Durrett and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-05-31 with Mathematics categories.
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.
The Number Of Sites Visited By A Random Walk On An Infinite Graph
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Author : Lee Randolph Gibson
language : en
Publisher:
Release Date : 2005
The Number Of Sites Visited By A Random Walk On An Infinite Graph written by Lee Randolph Gibson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.