The Annals of Probability

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

Dominic Schuhmacher and Kaspar Stucki

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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

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

First available in Project Euclid: 29 August 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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