Trapping of random walks on the line
type: Item
instance of: scholarly article
title: Trapping of random walks on the line
zbMATH Open document ID: 0586.60066
DOI: 10.1007/BF01012902
author: George H. Weiss
author: Shlomo Havlin
published in: Journal of Statistical Physics
publication date: 1984-01-01T00:00:00Z
review text: Several features of the trapping of random walks on a one-dimensional lattice are analyzed. The results of this investigation are as follows: (1) The correction term to the known asymptotic form for the survival probability to n steps is \(O((\lambda^ 2n)^{-1/3})\), where \(\lambda =-\ln (1-c)\), and c is the trap concentration. (2) The short time form for the survival probability is found to be \(\exp [-a(c)n^{1/2}]\). (3) The mean-square displacement of a surviving random walker is found to go like \(n^{2/3}\) for large n. (4) When the distribution of trap-free regions is changed so that very large regions are much rarer than for ideally random trap placement the asymptotic survival probability changes its dependence on n. One such model is studied.
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 60J70
zbMATH DE Number: 3940351
zbMATH Keywords: trapping
zbMATH Keywords: survival probabilities
zbMATH Keywords: asymptotic form for the survival probability
MaRDI profile type: Publication
cites work: On the number of distinct sites visited by a random walk
cites work: Q3241504
description: scientific article; zbMATH DE number 3940351