The Initial Configuration is Irrelevant for the Possibility of Mutual Unbounded Growth in the Two-Type Richardson Model
The Initial Configuration is Irrelevant for the Possibility of Mutual Unbounded Growth in the Two-Type Richardson Model
复制标题
初始配置与二型 Richardson 模型中相互无界增长的可能性无关
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
Olle Häggström
中科院分区：
文献类型：
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作者：
Maria Deijfen;Olle Häggström
两种类型理查森模型描述了 $mathbb{Z}^d$ 上两种竞争感染的增长。在时间 0 时，两个不相交的有限集 $xi_1,xi_2subset mathbb{Z}^d$ 分别感染 1 型和 2 型感染。然后，未受感染的站点会以与 1 (2) 型受感染的最近邻居的数量成比例的速度变为 1 (2) 型感染，并且一旦被感染，它将永远保持这种状态。宽松地说，本文的主要结果是，初始集 $xi_1$ 和 $xi_2$ 的选择与决定两种感染类型的相互无界增长事件是否具有正概率无关。
The two-type Richardson model describes the growth of two competing infections on $mathbb{Z}^d$. At time 0 two disjoint finite sets $xi_1,xi_2subset mathbb{Z}^d$ are infected with type 1 and type 2 infection respectively. An uninfected site then becomes type 1 (2) infected at a rate proportional to the number of type 1 (2) infected nearest neighbours and once infected it remains so forever. The main result in this paper is, loosely speaking, that the choice of the initial sets $xi_1$ and $xi_2$ is irrelevant in deciding whether or not the event of mutual unbounded growth for the two infection types has positive probability.