Critical behavior of the two-dimensional first passage time
type: Item
instance of: scholarly article
title: Critical behavior of the two-dimensional first passage time
zbMATH Open document ID: 0629.60109
DOI: 10.1007/BF01020583
published in: Journal of Statistical Physics
publication date: 1986-01-01T00:00:00Z
review text: We study the two-dimensional first passage problem in which bonds have zero and unit passage times with probability p and 1-p, respectively. We prove that as the zero-time bonds approach the percolation threshold \(p_ c\), the first passage time exhibits the same critical behavior as the correlation function of the underlying percolation problem. In particular, if the correlation length obeys \(\xi (p)\sim | p-p_ c|^ v\), then the first pasage time constant satisfies \(\mu (p)\sim | p-p_ c|^ v\). At \(p_ c\), where it has been asserted that the first passage time from 0 to x scales as \(| x|\) to a power \(\psi\) with \(0<\psi <1\), we show that the passage times grow like log\(| x|\), i.e., the fluid spreads exponentially rapidly.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 82B43
zbMATH DE Number: 4024482
zbMATH Keywords: critical behavior
zbMATH Keywords: two-dimensional first passage problem
zbMATH Keywords: percolation threshold
author: Jennifer T. Chayes
author: Lincoln Chayes
author: Rick Durrett
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4024482