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Publications [#243460] of Richard T. Durrett

Papers Published

  1. Durrett, R, Multicolor particle systems with large threshold and range, Journal of Theoretical Probability, vol. 5 no. 1 (January, 1992), pp. 127-152, Springer Nature, ISSN 0894-9840 [doi]
    (last updated on 2019/04/23)

    In this paper we consider the Greenberg-Hastings and cyclic color models. These models exhibit (at least) three different types of behavior. Depending on the number of colors and the size of two parameters called the threshold and range, the Greenberg-Hastings model either dies out, or has equilibria that consist of "debris" or "fire fronts". The phase diagram for the cyclic color models is more complicated. The main result of this paper, Theorem 1, proves that the debris phase exists for both systems. © 1992 Plenum Publishing Corporation.
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