Some peculiar properties of a particle system with sexual reproduction
Some peculiar properties of a particle system with sexual reproduction
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有性生殖粒子系统的一些特殊性质
DOI：
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发表时间：
1986
期刊：
影响因子：
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通讯作者：
R. Durrett
中科院分区：
文献类型：
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作者：
R. Durrett
本文的目的是描述一个具有有性繁殖（即需要两个粒子产生一个新的粒子）的二维生长模型，并将其性质与具有无性繁殖（即Harris（1978）和Griffeath（1979）意义下的可加过程）的类似模型的性质进行比较。本文报道的结果是与拉里·格雷合作获得的。Durrett和Gray（1985）给出了详细的证明，下面将其称为DG（1985）。在这两个模型中，系统在时刻t的状态是St，是Z2的子集，粒子以速率1死亡，即如果xe ~t，则P（x ~+61 ~t）= 6 + 0（6）as 6+0，其中~t = °（~6：s~t）=到时刻t为止由过程产生的O场.这两个模型的区别在于它们的出生率，可以描述如下：
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: