Some Peculiar Properties of a Particle System with Sexual Reproduction
نویسنده
چکیده
The purpose of this paper is to describe a two dimensional growth model with sexual reproduction (i.e. two particles are needed to produce a new one) and contrast its properties with those of a similar model with asexual reproduction (i.e. an additive process in the sense of Harris (1978) and Griffeath (1979)). The results reported here were obtained in collaboration with Larry Gray. Detailed proofs are given in Durrett and Gray (1985), a source which will be referred to as DG(1985) below. In both models the state of the system at time t is S t a subset of Z 2, and particles die at rate one, that is, if x e ~t then P(x ~ ~+61~t ) = 6 + 0(6) as 6+0, where ~t = °(~6:s~t) = the Ofield generated by the process up to time t. The two models then are distinguished by their birth rates which can be described as follows:
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تاریخ انتشار 2006