Journal of Theoretical Probability

, Volume 28, Issue 4, pp 1447–1467 | Cite as

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

  • Xiaofeng Xue


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 \(0\) is introduced.


Contact process Threshold-one Critical value Asymptotic behavior 

Mathematics Subject Classification (2010)

60K35 82C22 



This work is supported by the National Basic Research Program of China (2011CB808000), National Natural Science Foundation of China (No. 11001004), and China Scholarship Council (No. 201206010097)


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.School of Mathematical SciencesPeking UniversityBeijingChina

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