RANDOM WALKS ON INFINITE GRAPHS AND GROUPS

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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 bas on various aspects of the behaviour of the random walk. Conversely, random walks may also be seen as a useful tool 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 processes and related topics.

TÉLÉCHARGER
AUTEUR Wolfgang Woess
DATE DE PUBLICATION 2000-Jan-31
TAILLE DU FICHIER 10,74 MB
LIRE EN LIGNE

Graduate course: Probability and Geometry on Groups

5. Random Walks - YouTube

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.

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