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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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CTRW and aging phenomena

CTRW and aging phenomena

Chapter:
(p.54) 4 CTRW and aging phenomena
Source:
First Steps in Random Walks
Author(s):

J. Klafter

I.M. Sokolov

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199234868.003.0004

The CTRW process with diverging mean waiting time is non‐stationary. Its properties depend explicitly on the time passed from the beginning of motion (i.e. on the age of the system), and therefore, if the observation does not start at the time of preparation of the process, on this time. Aging phenomena are related to the distribution of the waiting time for the first step after the beginning of observation (forward waiting time), which shows nontrivial behavior (inspection paradox). Physical consequences of aging include death of linear response of the system to external oscillating fields and nontrivial behavior of moving time averages over single trajectories mimicking the one in normal diffusion.

Keywords:   aging, forward waiting time, inspection paradox, moving time average, death of linear response

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