Random Walks And Discrete Potential Theory
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Random Walks and Discrete Potential Theory
Author: M. Picardello
language: en
Publisher: Cambridge University Press
Release Date: 1999-11-18
Comprehensive and interdisciplinary text covering the interplay between random walks and structure theory.
Random Walks on Infinite Graphs and Groups
Author: Wolfgang Woess
language: en
Publisher: Cambridge University Press
Release Date: 2000-02-13
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.
Quantum Potential Theory
This book offers the revised and completed notes of lectures given at the 2007 conference, "Quantum Potential Theory: Structures and Applications to Physics." These lectures provide an introduction to the theory and discuss various applications.