WIAS Preprint No. 3126, (2024)

The variational principle for a marked Gibbs point process with infinite-range multibody interactions


Authors

  • Jahnel, Benedikt
    ORCID: 0000-0002-4212-0065
  • Köppl, Jonas
    ORCID: 0000-0001-9188-1883
  • Steenbeck, Yannic
  • Zass, Alexander
    ORCID: 0000-0001-6124-842X

2020 Mathematics Subject Classification

  • 82C22 60K35

Keywords

  • Variational principle, specific entropy, point processes, Gibbs point process, interacting particle systems, depletion interaction

DOI

10.20347/WIAS.PREPRINT.3126

Abstract

We prove the Gibbs variational principle for the Asakura?Oosawa model in which particles of random size obey a hardcore constraint of non-overlap and are additionally subject to a temperature-dependent area interaction. The particle size is unbounded, leading to infinite-range interactions, and the potential cannot be written as a k-body interaction for fixed k. As a byproduct, we also prove the existence of infinite-volume Gibbs point processes satisfying the DLR equations. The essential control over the influence of boundary conditions can be established using the geometry of the model and the hard-core constraint.

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