Asymptotic density in a threshold coalescing and annihilating random walk
成果类型：
Article
署名作者：
Stephenson, D
署名单位：
Cornell University
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1008956326
发表日期：
2001
页码：
137-175
关键词：
摘要：
We consider an interacting random walk on Z (d) where particles interact only at times when a particle jumps to a site at which there are at least n - 1 other particles present. If there are i greater than or equal to n - 1 particles present, then the particle coalesces (is removed from the system) with probability ci and annihilates (is removed along with another particle) with probability ai. We call this process the n-threshold randomly coalescing and annihilating random walk. We show that, for n greater than or equal to 3, if both a(i) and a(i) + c(i) are increasing in i and if the dimension d is at least 2n + 4, then P(the origin is occupied at time t) - C(d. n)t - 1/n-1, E(number of particles at the origin at time t) - C(d, n)t - 1/n-1. The constants C(d, n) are explicitly identified. The proof is an extension of a result obtained by Kesten and van den Berg for the 2-threshold coalescing random walk and is based on an approximation for dE(t)/dt.
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