Space representation of stochastic processes with delay

Silvio R. Dahmen, Haye Hinrichsen, and Wolfgang Kinzel
Phys. Rev. E 77, 031106 – Published 6 March 2008

Abstract

We show that a time series xt evolving by a nonlocal update rule xt=f(xtn,xtk) with two different delays k<n can be mapped onto a local process in two dimensions with special time-delayed boundary conditions, provided that n and k are coprime. For certain stochastic update rules exhibiting a nonequilibrium phase transition, this mapping implies that the critical behavior does not depend on the short delay k. In these cases, the autocorrelation function of the time series is related to the critical properties of the corresponding two-dimensional model.

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  • Received 28 March 2007

DOI:https://doi.org/10.1103/PhysRevE.77.031106

©2008 American Physical Society

Authors & Affiliations

Silvio R. Dahmen1,2, Haye Hinrichsen1, and Wolfgang Kinzel1

  • 1Fakultät für Physik und Astronomie, Universität Würzburg, Am Hubland, D-97074 Würzburg, Germany
  • 2Instituto de Física da UFRGS, Avenida Bento Gonçalves 9500, 91501-970 Porto Alegre, Brazil

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Vol. 77, Iss. 3 — March 2008

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