#
POISSON LIMITS FOR PAIRWISE AND AREA INTERACTION POINT PROCESSES

##
By S. Rao Jammalamadaka and Mathew D. Penrose.

Suppose *n* particles *x*_{i} in a region of the plane
(possibly representing biological individuals - trees, organisms)
which is weighted, relative to an i.i.d. distribution in the plane,
by a factor
of exp (*-S*),
where *S* denotes the sum over all distinct pairs *i,j*
of
the quanitity
*f (n(x*_{i}-x_{j})), with *f*
a specified function of compact support.
We obtain a Poisson process limit for the collection of
rescaled interparticle distances as *n* becomes large.
We also give corresponding results for the case of several types
of particles, representing different species,
and also for
the area-interaction (Widom-Rowlinson) point process of interpenetrating
spheres.
Advances in Applied Probability 32, 75-85 (2000).