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Asymptotic Behavior of Critical Infection Rates for Threshold-One Contact Processes on Lattices and Regular Trees

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  • Xiaofeng Xue

    (Peking University)

Abstract

In this paper, we are concerned with threshold-one contact processes on lattices and regular trees. We show that the critical infection rate for the process to survive is approximately inversely proportional to the degree of the graph. To prove this main result, a crucial lemma about the chance for a simple random walk to return to $$0$$ 0 is introduced.

Suggested Citation

  • Xiaofeng Xue, 2015. "Asymptotic Behavior of Critical Infection Rates for Threshold-One Contact Processes on Lattices and Regular Trees," Journal of Theoretical Probability, Springer, vol. 28(4), pages 1447-1467, December.
    • Handle: RePEc:spr:jotpro:v:28:y:2015:i:4:d:10.1007_s10959-014-0544-1
    DOI: 10.1007/s10959-014-0544-1
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    References listed on IDEAS

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    1. Andjel, Enrique D. & Liggett, Thomas M. & Mountford, Thomas, 1992. "Clustering in one-dimensional threshold voter models," Stochastic Processes and their Applications, Elsevier, vol. 42(1), pages 73-90, August.
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