Random walks on percolation with a topological bias: Decay of the probability density

Julia Dräger and Armin Bunde

Physica A: Statistical Mechanics and its Applications, 1999, vol. 266, issue 1, 62-66

Abstract: We investigate random walks on the infinite percolation cluster at the critical concentration pc under the influence of a topological bias field, where the hopping rates towards larger chemical distances ℓ from the origin of the walk are increased. We find that the root mean square displacement evolves with time as R(t)∼(lnt)γ(ε) where γ(ε) depends on the strength ε of the field. The probability P(r,t) to find the random walker after t time-steps on a site at distance r from its starting point decays asymptotically as −lnP(r,t)∼−ru(t) with u(t)=ln(t)/(ln(t)−γ(ε)) and approaches a simple exponential for asymptotic large time. A similiar picture arises for the behavior of the probability density P(ℓ,t), where ℓ is the chemical (shortest path) distance from the origin of the random walk.

Keywords: Random walks; Percolation Systems; Topological bias Field (search for similar items in EconPapers)
Date: 1999
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437198005755
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:266:y:1999:i:1:p:62-66

DOI: 10.1016/S0378-4371(98)00575-5

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().