We obtain upper bounds for the total variation distance between the
distributions of two Gibbs point processes in a very general setting.
Applications are provided to various well-known processes and settings from
spatial statistics and statistical physics, including the comparison of two
Lennard-Jones processes, hard core approximation of an area interaction process
and the approximation of lattice processes by a continuous Gibbs process. Our
proof of the main results is based on Stein's method. We construct an explicit
coupling between two spatial birth-death processes to obtain Stein factors, and
employ the Georgii-Nguyen-Zessin equation for the total bound.Comment: Published in at http://dx.doi.org/10.1214/13-AOP895 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
