Exponential Decay for Subcritical Contact and Percolation Processes
Open Access
- 1 July 1991
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Probability
- Vol. 19 (3) , 984-1009
- https://doi.org/10.1214/aop/1176990332
Abstract
We study the contact process, together with a version of the percolation process with one continuously varying coordinate. It is proved here that the radius of the infected cluster has an exponentially decaying tail throughout the subcritical phase. The same is true of the Lebesgue measure (in space-time) of this cluster. Certain critical-exponent inequalities are derived and the critical point of the percolation process in two dimensions is determined exactly.Keywords
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