LIMIT THEOREMS FOR MONOTONIC PARTICLE SYSTEMS AND SEQUENTIAL DEPOSITION
By Mathew D. Penrose
We prove spatial laws of large numbers and central limit theorems
for the ultimate number of adsorbed particles in a large class of
multidimensional random and cooperative sequential adsorption schemes
on the lattice, and also for
the Johnson-Mehl model of birth, linear growth and spatial exclusion
in the continuum. The lattice result is also applicable
to certain telecommunications networks. The proofs are based
on a general law of large numbers and central limit
theorem for sums of random variables determined by
the restriction of white noise process
to large spatial regions.