Critical behavior of the two-dimensional first passage time


Journal Article

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 pc, 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 ξ(p) ∼|p-pc|-v, then the first passage time constant satisfies μ(p)∼|p-pc|v. At pc, where it has been asserted that the first passage time from 0 to x scales as |x| to a power ψ with 0<ψ<1, we show that the passage times grow like log |x|, i.e., the fluid spreads exponentially rapidly. © 1986 Plenum Publishing Corporation.

Full Text

Duke Authors

Cited Authors

  • Chayes, JT; Chayes, L; Durrett, R

Published Date

  • December 1, 1986

Published In

Volume / Issue

  • 45 / 5-6

Start / End Page

  • 933 - 951

Electronic International Standard Serial Number (EISSN)

  • 1572-9613

International Standard Serial Number (ISSN)

  • 0022-4715

Digital Object Identifier (DOI)

  • 10.1007/BF01020583

Citation Source

  • Scopus