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Asymptotic behaviors of upper invariant measures for high-dimensional threshold-one contact processes

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  • Xue, Xiaofeng

Abstract

In this paper, we are concerned with the threshold-one contact process on Zd. We give a limit theorem of the probability of the event that the origin is occupied for the upper invariant measure of the process as the dimension d grows to infinity while the infection rate is inversely proportional to d. A branching process and a SIR model are introduced as auxiliary processes for the proof of our main result.

Suggested Citation

  • Xue, Xiaofeng, 2019. "Asymptotic behaviors of upper invariant measures for high-dimensional threshold-one contact processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 527(C).
    • Handle: RePEc:eee:phsmap:v:527:y:2019:i:c:s0378437119307708
    DOI: 10.1016/j.physa.2019.121291
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