Journal of Statistical Physics

, Volume 45, Issue 5–6, pp 933–951 | Cite as

Critical behavior of the two-dimensional first passage time

  • J. T. Chayes
  • L. Chayes
  • R. Durrett


We study the two-dimensional first passage problem in which bonds have zero and unit passage times with probabilityp and 1−p, respectively. We prove that as the zero-time bonds approach the percolation thresholdpc, the first passage time exhibits the same critical behavior as the correlation function of the underlying percolation problem. In particular, if the correlation length obeysξ(p)¦p−pc¦−v, then the first passage time constant satisfiesμ(p)∼¦p−pc¦v. At pc, where it has been asserted that the first passage time from 0 tox 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.

Key words

First passage time critical behavior two dimensions 


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Copyright information

© Plenum Publishing Corporation 1986

Authors and Affiliations

  • J. T. Chayes
    • 1
  • L. Chayes
    • 1
  • R. Durrett
    • 2
  1. 1.Laboratory of Atomic and Solid State PhysicsCornell UniversityIthaca
  2. 2.Department of MathematicsCornell UniversityIthaca

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