Exponential Decay for Subcritical Contact and Percolation Processes
Bezuidenhout, Carol ; Grimmett, Geoffrey
Ann. Probab., Tome 19 (1991) no. 4, p. 984-1009 / Harvested from Project Euclid
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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.
Publié le : 1991-07-14
Classification:  Contact process,  percolation,  60K35 
@article{1176990332,
     author = {Bezuidenhout, Carol and Grimmett, Geoffrey},
     title = {Exponential Decay for Subcritical Contact and Percolation Processes},
     journal = {Ann. Probab.},
     volume = {19},
     number = {4},
     year = {1991},
     pages = { 984-1009},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176990332}
}

Bezuidenhout, Carol; Grimmett, Geoffrey. Exponential Decay for Subcritical Contact and Percolation Processes. Ann. Probab., Tome 19 (1991) no. 4, pp.  984-1009. http://gdmltest.u-ga.fr/item/1176990332/