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First Steps in Random WalksFrom Tools to Applications$
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J. Klafter and I. M. Sokolov

Print publication date: 2011

Print ISBN-13: 9780199234868

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780199234868.001.0001

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Continuous-time random walks

Continuous-time random walks

Chapter:
(p.36) 3 Continuous-time random walks
Source:
First Steps in Random Walks
Author(s):

J. Klafter

I.M. Sokolov

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199234868.003.0003

Up to now the book has considered the displacement and the return properties of a walker as functions of the number of steps. In physics and chemistry we however are mostly interested in the behavior of the corresponding properties as functions of time. Translating steps into time and back is done by assuming that a walker waits for the next step for a time t distributed according to a known density. Such a process is known as continuous time random walk (CTRW). The CTRW formalism is used to calculate the distribution of displacements, as well as first passage and return times. Special attention is paid to the case when the mean waiting time diverges, as a one often used in applications.

Keywords:   continuous‐time random walks, waiting times, power‐law waiting time distributions, mean number of steps, first passage and return probabilities in CTRW

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