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A CENTRAL LIMIT THEOREM WITH APPLICATIONS TO PERCOLATION,
EPIDEMICS AND BOOLEAN MODELS

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By Mathew D. Penrose.

Suppose *X = (X*_{x})_{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
``stabilization''
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.