Random walk on a random walk

K.W. Kehr and R. Kutner

Physica A: Statistical Mechanics and its Applications, 1982, vol. 110, issue 3, 535-549

Abstract: The authors investigate the random walk of a particle on a one-dimensional chain which has been constructed by a random-walk procedure. Exact expressions are given for the mean-square displacement and the fourth moment after n steps. The probability density after n steps is derived in the saddle-point approximation, for large n. These quantities have also been studied by numerical simulation. The extension to continuous time has been made where the particle jumps according to a Poisson process. The exact solution for the self-correlation function has been obtained in the Fourier and Laplace domain. The resulting frequency-dependent diffusion coefficient and incoherent dynamical structure factor have been discussed. The model of random walk on a random walk is applied to self-diffusion in the concentrated one-dimensional lattice gas where the correct asymptotic behavior is found.

Date: 1982
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:110:y:1982:i:3:p:535-549

DOI: 10.1016/0378-4371(82)90067-X

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