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On some threshold-one attractive interacting particle systems on homogeneous trees

Part of: Special processes

Published online by Cambridge University Press:  04 September 2020

Y. X. Mu  and
Y. Zhang
Y. X. Mu*
Affiliation:
Peking University
Y. Zhang*
Affiliation:
Peking University
*
*Postal address: School of Mathematical Sciences, Peking University, Beijing 100871, P. R. China. Email address: muyingxin@pku.edu.cn
*Postal address: School of Mathematical Sciences, Peking University, Beijing 100871, P. R. China. Email address: muyingxin@pku.edu.cn
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Abstract

We consider the threshold-one contact process, the threshold-one voter model and the threshold-one voter model with positive spontaneous death on homogeneous trees $\mathbb{T}_d$ , $d\ge 2$ . Mainly inspired by the corresponding arguments for the contact process, we prove that the complete convergence theorem holds for these three systems under strong survival. When the system survives weakly, complete convergence may also hold under certain transition and/or initial conditions.

Keywords

Complete convergence theoremthreshold-one processeshomogeneous trees

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 57 , Issue 3 , September 2020 , pp. 866 - 898
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Copyright
© Applied Probability Trust 2020

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