On the asymptotic geometrical behaviour of percolation processes
- 1 June 1980
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 17 (2) , 385-402
- https://doi.org/10.2307/3213028
Abstract
In this paper the global behaviour of percolation processes on thed-dimensional square lattice is studied. Using techniques of Richardson (1973) we prove, under weak moment assumptions on the time coordinate distribution, the following result. There exists a norm N(·) onRdsuch that, for all 0 <ε< 1, we have that almost surely for all sufficiently largettheN-ball of radius (1 –ε)tis contained inη, (the set of all sites occupied by timet) andη, is contained in theN-ball of radius (1 +ε)t. Richardson (1973) derived the corresponding ‘in probability' result for a class of spread processes onRd, satisfying certain conditions.Keywords
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