Mathematics > Probability
[Submitted on 13 Dec 2018 (v1), last revised 21 Feb 2020 (this version, v3)]
Title:On some threshold-one attractive interacting particle systems on homogeneous trees
View PDFAbstract:In this paper, we consider the threshold-one contact process and the threshold-one voter model w/o spontaneous death on homogeneous trees $\mathbb{T}_d$, $d\ge 2$. Mainly inspired by the corresponding arguments for ordinary contact processes, we prove that the complete convergence theorem holds for these three systems under strong survival. When the systems survives weakly, complete convergence may also hold under certain transition and/or initial conditions.
Submission history
From: Mu Yingxin [view email][v1] Thu, 13 Dec 2018 05:38:31 UTC (25 KB)
[v2] Tue, 21 May 2019 05:13:31 UTC (27 KB)
[v3] Fri, 21 Feb 2020 17:39:46 UTC (384 KB)
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