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Random walk on a linear chain with a quenched distribution of jump lengths

Ryszard Kutner 1,  Philipp Maass 2

1. Faculty of Physics, University of Warsaw (FPUW), Pasteura 5, Warsaw 02-093, Poland
2. Universität Konstanz, Universitätsstr. 10, Konstanz 78457, Germany

Abstract
We study the random walk of a particle on a linear chain, where a jump length 1 or 2 is assigned randomly to each lattice site with probability p1 and p2=1-p1, respectively. We find that the probability peff1 for the particle to be at a site with jump length 1 is different from p1, which causes the diffusion coefficient D to differ from the mean-field result. A theory is developed that allows us to calculate peff1 and D for all values of p1. In the limit p1→0, the theory yields a nonanalytic dependence of peff1 on p1,peff1∼-p21ln p1

Physical Review E 55 (1997), 71.

 

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Presentation: Article at Econophysics group of Ryszard Kutner, by Ryszard Kutner
See On-line Journal of Econophysics group of Ryszard Kutner

Submitted: 2016-03-29 09:41
Revised:   2016-03-29 09:52