The Annals of Probability

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

Dominic Schuhmacher and Kaspar Stucki

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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.

Article information

Source
Ann. Probab., Volume 42, Number 5 (2014), 1911-1951.

Dates
First available in Project Euclid: 29 August 2014

Permanent link to this document
https://projecteuclid.org/euclid.aop/1409319470

Digital Object Identifier
doi:10.1214/13-AOP895

Mathematical Reviews number (MathSciNet)
MR3262495

Zentralblatt MATH identifier
1322.60060

Subjects
Primary: 60G55: Point processes
Secondary: 60J75: Jump processes 82B21: Continuum models (systems of particles, etc.)

Keywords
Conditional intensity pairwise interaction process birth–death process Stein’s method total variation distance

Citation

Schuhmacher, Dominic; Stucki, Kaspar. Gibbs point process approximation: Total variation bounds using Stein’s method. Ann. Probab. 42 (2014), no. 5, 1911--1951. doi:10.1214/13-AOP895. https://projecteuclid.org/euclid.aop/1409319470


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