Department of Mathematics
 Search | Help | Login | pdf version | printable version

Math @ Duke





.......................

.......................


Publications [#243443] of Richard T. Durrett

Papers Published

  1. Chayes, JT; Chayes, L; Durrett, R, Inhomogeneous percolation problems and incipient infinite clusters, Journal of Physics A: Mathematical and General, vol. 20 no. 6 (1987), pp. 1521-1530, ISSN 0305-4470 [doi]
    (last updated on 2017/12/15)

    Abstract:
    The authors consider inhomogeneous percolation models with density p c+f(x) and examine the forms of f(x) which produce incipient structures. Taking f(x) approximately= mod x mod - lambda and assuming the existence of a correlation length exponent v for the homogeneous percolation model, they prove that in d=2, the borderline value of lambda is lambda b=1/v. If lambda >1/v then, with probability one, there is no infinite cluster, while if lambda <1/v then, with positive probability, the origin is part of an infinite cluster. This result sheds some light on numerical and theoretical predictions of certain properties of incipient infinite clusters. Furthermore, for d>2, the models studied suggest what sort of 'incipient objects' should be examined in random surface models.

 

dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320