## Electronic Journal of Probability

### Disagreement percolation for the hard-sphere model

Hofer-Temmel Christoph

#### Abstract

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.

#### Article information

Source
Electron. J. Probab., Volume 24 (2019), paper no. 91, 22 pp.

Dates
Accepted: 12 May 2019
First available in Project Euclid: 10 September 2019

https://projecteuclid.org/euclid.ejp/1568080871

Digital Object Identifier
doi:10.1214/19-EJP320

#### Citation

Christoph, Hofer-Temmel. Disagreement percolation for the hard-sphere model. Electron. J. Probab. 24 (2019), paper no. 91, 22 pp. doi:10.1214/19-EJP320. https://projecteuclid.org/euclid.ejp/1568080871

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