Summary
In the threshold contact process on thed-dimensional integer lattice with ranger, healthy sites become infected at rate λ if they have at least one infectedr-neighbour, and recover at rate 1. We show that the critical valueλ c (r) is asymptotic tor −d μ c asr→∞, where μ c is the critical value of the birth rate μ for a continuum threshold contact process which may be described in terms of an oriented continuous percolation model driven by a Poisson process of rate μ ind+1 dimensions. We have bounds of 0.7320 < μ c < 3 ford=1.
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Penrose, M.D. The threshold contact process: A continuum limit. Probab. Th. Rel. Fields 104, 77–95 (1996). https://doi.org/10.1007/BF01303804
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DOI: https://doi.org/10.1007/BF01303804
Mathematics Subject Classfication
- 60K35
- 60F99