Random Walks on Infinite Graphs and Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Random Walks on Infinite Graphs and Groups write by Wolfgang Woess. This book was released on 2000-02-13. Random Walks on Infinite Graphs and Groups available in PDF, EPUB and Kindle. 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
Random walks on infinite graphs and groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Random walks on infinite graphs and groups write by Wolfgang Woess. This book was released on 1991. Random walks on infinite graphs and groups available in PDF, EPUB and Kindle.
Random Walks on Infinite Groups
Random Walks on Infinite Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Random Walks on Infinite Groups write by Steven P. Lalley. This book was released on 2023-05-08. Random Walks on Infinite Groups available in PDF, EPUB and Kindle. 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.
Probability on Trees and Networks
Probability on Trees and Networks - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Probability on Trees and Networks write by Russell Lyons. This book was released on 2017-01-20. Probability on Trees and Networks available in PDF, EPUB and Kindle. 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.
Probability on Graphs
Probability on Graphs - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Probability on Graphs write by Geoffrey Grimmett. This book was released on 2018-01-25. Probability on Graphs available in PDF, EPUB and Kindle. 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.
