Large-Scale Molecular Systems pp 477-482 | Cite as

# Dynamical Exponents for 1-D Random-Random Directed Walks

Chapter

## Abstract

We consider the one-dimensional random directed walk on a disordered lattice described by the following master equation :
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) p

$$\frac{{\text{dp}_\text{n} }}{{\text{dt}}}\text{ = - W}_\text{n} \text{P}_\text{n} \text{ + W}_{\text{n - 1}} \text{P}_{\text{n - 1}}$$

(1)

_{n}(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.## Keywords

Dynamical Exponent Asymmetric Model Directed Walk Final Dynamic Generate Function Method
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## References

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## Copyright information

© Plenum Press, New York 1991