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Variable survival exponents in history-dependent random walks: hard movable reflector

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dc.creator Dickman Ronald
dc.creator Araujo Jr. Francisco Fontenele
dc.creator ben-Avraham Daniel
dc.date 2003
dc.date.accessioned 2013-06-01T10:28:04Z
dc.date.available 2013-06-01T10:28:04Z
dc.date.issued 2013-06-01
dc.identifier http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0103-97332003000300006
dc.identifier http://www.doaj.org/doaj?func=openurl&genre=article&issn=01039733&date=2003&volume=33&issue=3&spage=450
dc.identifier.uri http://koha.mediu.edu.my:8181/jspui/handle/123456789/8186
dc.description We review recent studies demonstrating a nonuniversal (continuously variable) survival exponent for history-dependent random walks, and analyze a new example, the hard movable partial reflector. These processes serve as simplified models of infection in a medium with a history-dependent susceptibility, and for spreading in systems with an infinite number of absorbing configurations. The memory may take the form of a historydependent step length, or be the result of a partial reflector whose position marks the maximum distance the walker has ventured from the origin. In each case, a process with memory is rendered Markovian by a suitable expansion of the state space. Asymptotic analysis of the probability generating function shows that, for large t, the survival probability decays as S(t) ~ t -d, where d varies with the parameters of the model. We report new results for a hard partial reflector, i.e., one that moves forward only when the walker does. When the walker tries to jump to the site R occupied by the reflector, it is reflected back with probability r, and stays at R with probability 1 - r; only in the latter case does the reflector move (R ® R+1). For this model, d = 1/2(1 - r), and becomes arbitrarily large as r approaches 1. This prediction is confirmed via iteration of the transition matrix, which also reveals slowly-decaying corrections to scaling.
dc.publisher Sociedade Brasileira de Física
dc.source Brazilian Journal of Physics
dc.title Variable survival exponents in history-dependent random walks: hard movable reflector

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