文章基本信息

标题：Two limit theorems for the high-dimensional two-stage contact process
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作者：Xiaofeng Xue
期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2020
卷号：17
期号：2
页码：825
DOI：10.30757/ALEA.v17-32
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：In this paper we are concerned with the two-stage contact process introduced by Krone (1999) on a high-dimensional lattice. By comparing this process with an auxiliary model which is a linear system, we obtain two limit theorems for this process as the dimension of the lattice grows to infinity. The first theorem is about the upper invariant law of the process. The second theorem is about asymptotic behavior of the critical value of the process. These two theorems can be considered as extensions of their counterparts for the basic contact processes proved by Griffeath (1983) and Schonmann and Vares (1986).
其他关键词：Two-stage, contact process, critical value, invariant measure. Research supported by the National Natural Science Foundation of China.