Dynamical Exponents for 1-D Random-Random Directed Walks

  • Claude Aslangul
  • Marc Barthelemy
  • Noëlle Pottier
  • Daniel Saint-James
Part of the NATO ASI Series book series (NSSB, volume 258)


We consider the one-dimensional random directed walk on a disordered lattice described by the following master equation :
$$\frac{{\text{dp}_\text{n} }}{{\text{dt}}}\text{ = - W}_\text{n} \text{P}_\text{n} \text{ + W}_{\text{n - 1}} \text{P}_{\text{n - 1}}$$
This equation is the directed version of the usual master equation which describes a random process in which the variable of interest can only increase (see for instance ref. 1 for the symmetric case and refs. 2 and 3 for recent reviews on asymmetric models). In eq. (1) pn(t) denotes the probability to be at site labelled n at time t, the W’s are non-negative quantities chosen independently at random in a given probability distribution ρ(W). The W’s are assumed to be time-independent (quenched disorder). The general both-way asymmetric walk is believed to be asymptotically similar to a directed walk on a renormalized lattice 4,5; the directed walk is thus expected to generate the basic features of the general problem in a simplified framework.


Dynamical Exponent Asymmetric Model Directed Walk Final Dynamic Generate Function Method 
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Copyright information

© Plenum Press, New York 1991

Authors and Affiliations

  • Claude Aslangul
    • 1
  • Marc Barthelemy
    • 1
  • Noëlle Pottier
    • 1
  • Daniel Saint-James
    • 2
    • 3
  1. 1.GPS, Tour 23Université Paris VIIParis Cedex 05France
  2. 2.Laboratoire de Physique StatistiqueCollège de FranceParis Cedex 05France
  3. 3.Université Paris VIIFrance

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