Open Access
2019 Disagreement percolation for the hard-sphere model
Hofer-Temmel Christoph
Electron. J. Probab. 24: 1-22 (2019). DOI: 10.1214/19-EJP320


Disagreement percolation connects a Gibbs lattice gas and i.i.d. site percolation on the same lattice such that non-percolation implies uniqueness of the Gibbs measure. This work generalises disagreement percolation to the hard-sphere model and the Boolean model. Non-percolation of the Boolean model implies the uniqueness of the Gibbs measure and exponential decay of pair correlations and finite volume errors. Hence, lower bounds on the critical intensity for percolation of the Boolean model imply lower bounds on the critical activity for a (potential) phase transition. These lower bounds improve upon known bounds obtained by cluster expansion techniques. The proof uses a novel dependent thinning from a Poisson point process to the hard-sphere model, with the thinning probability related to a derivative of the free energy.


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Hofer-Temmel Christoph. "Disagreement percolation for the hard-sphere model." Electron. J. Probab. 24 1 - 22, 2019.


Received: 19 March 2018; Accepted: 12 May 2019; Published: 2019
First available in Project Euclid: 10 September 2019

zbMATH: 1426.82015
MathSciNet: MR4003144
Digital Object Identifier: 10.1214/19-EJP320

Primary: 82B21
Secondary: 60D05 , 60E15 , 60G55 , 60K35 , 82B43

Keywords: absence of phase transition , Boolean model , dependent thinning , disagreement percolation , hard-sphere model , stochastic domination , unique Gibbs measure

Vol.24 • 2019
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