Asymptotics for the Wiener sausage with drift
type: Item
instance of: scholarly article
title: Asymptotics for the Wiener sausage with drift
zbMATH Open document ID: 0586.60076
DOI: 10.1007/BF01845643
author: B. George
publication date: 1986-01-01T00:00:00Z
review text: A particle is considered which moves in \({\mathbb{R}}^ d\) according to a Brownian motion with drift \(h\neq 0\). The space is assumed to contain random traps. The probability of survival of the particle up to time T decays exponentially as \(T\to \infty\) with a positive decay rate \(\lambda\). \(\lambda\) is shown to be a non-analytic function of \(| h|\). For small \(| h|\) the decay rate is given by \(\lambda (h)=2^{-1}| h|^ 2\); but if \(| h|\) exceeds a certain critical value, \(\lambda\) (h) depends also on the parameters describing trapping. Upper and lower bounds for \(\lambda\) (h) are given, which imply the asymptotic linearity of \(\lambda\) (h) for large \(| h|.\) The critical point marks a transition from localized to delocalized behavior. A variational formula for the decay rate is given on the level of generalized processes, which elucidates the mathematical mechanism behind observations made earlier by Grassberger and Procaccia on the basis of computer simulations.
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 3940361
zbMATH Keywords: Wiener sausage with drift
zbMATH Keywords: decay rate
zbMATH Keywords: asymptotic linearity
zbMATH Keywords: transition from localized to delocalized behavior
zbMATH Keywords: variational formula for the decay rate
MaRDI profile type: Publication
cites work: Asymptotics for the wiener sausage
cites work: Q3870044
cites work: Q3259971
cites work: Q3662379
cites work: Q4725439
cites work: Electrostatic capacity, heat flow, and brownian motion
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 3940361