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

Xiaofeng Xue ()
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Xiaofeng Xue: Peking University

Journal of Theoretical Probability, 2015, vol. 28, issue 4, 1447-1467

Abstract: 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.

Keywords: Contact process; Threshold-one; Critical value; Asymptotic behavior; 60K35; 82C22 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10959-014-0544-1

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