Gibbs point process approximation: Total variation bounds using Stein's method

Abstract

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.

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)

References in corpus (1)

• Entropy decay for interacting systems via the Bochner--Bakry--Emery approach

Cited by in corpus (7)

• Functional Poisson approximation in Kantorovich-Rubinstein distance with applications to U-statistics and stochastic geometry
• Cluster expansions for Gibbs point processes
• On the uniqueness of Gibbs distributions with a non-negative and subcritical pair potential
• Stability of gas measures under perturbations and discretizations
• Stein's method and Papangelou intensity for Poisson or Cox process approximation
• Structural properties of Gibbsian point processes in abstract spaces
• Multivariate Poisson and Poisson process approximations with applications to Bernoulli sums and $U$-statistics