Publications [#243447] of Richard T. Durrett

Papers Published

1. Bramson, M; Durrett, R, A simple proof of the stability criterion of Gray and Griffeath, Probability Theory and Related Fields, vol. 80 no. 2 (December, 1988), pp. 293-298, Springer Nature America, Inc, ISSN 0178-8051
   (last updated on 2024/04/19)

   Abstract:
   Gray and Griffeath studied attractive nearest neighbor spin systems on the integers having "all 0's" and "all 1's" as traps. Using the contour method, they established a necessary and sufficient condition for the stability of the "all 1's" equilibrium under small perturbations. In this paper we use a renormalized site construction to give a much simpler proof. Our new approach can be used in many situations as a substitute for the contour method. © 1988 Springer-Verlag.