Math @ Duke

Publications [#243440] of Richard T. Durrett
Papers Published
 Chayes, JT; Chayes, L; Durrett, R, Critical behavior of the twodimensional first passage time,
Journal of Statistical Physics, vol. 45 no. 56
(December, 1986),
pp. 933951, Springer Nature, ISSN 00224715 [doi]
(last updated on 2019/06/19)
Abstract: We study the twodimensional first passage problem in which bonds have zero and unit passage times with probability p and 1p, respectively. We prove that as the zerotime 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) ∼ppcv, then the first passage time constant satisfies μ(p)∼ppcv. 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.


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