A CENTRAL LIMIT THEOREM WITH APPLICATIONS TO PERCOLATION,
EPIDEMICS AND BOOLEAN MODELS
By Mathew D. Penrose.
Suppose X = (Xx)x in Zd
is a white noise process,
and H(B), defined for each lattice box B, is determined
in a stationary way by the restriction of X to B. Using
a martingale approach, we prove a central limit theorem (CLT) for
H as B becomes large, subject to H satisfying a
condition. This CLT is then applied to component counts
for percolation and Boolean models, to the size of the big
cluster for percolation on a box, and to the final size of a spatial epidemic.