| Abstrakt: |
In the threshold contact process on the d-dimensional integer lattice with range r, healthy sites become infected at rate λ if they have at least one infected r-neighbour, and recover at rate 1. We show that the critical value λ( r) is asymptotic to r μ as r→∞, where μ 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 in d+1 dimensions. We have bounds of 0.7320 < μ < 3 for d=1. [ABSTRACT FROM AUTHOR] |
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