WIAS Preprint No. 2859, (2021)

Gibbs point processes on path space: Existence, cluster expansion and uniqueness


Authors

  • Zass, Alexander
    ORCID: 0000-0001-6124-842X

2020 Mathematics Subject Classification

  • 60K35 60G55 60K35 60G55

Keywords

  • Marked Gibbs point process, DLR equations, uniqueness, cluster expansion, infinite-dimensional diffusion

DOI

10.20347/WIAS.PREPRINT.2859

Abstract

We study a class of infinite-dimensional diffusions under Gibbsian interactions, in the context of marked point configurations: The starting points belong to R^d, and the marks are the paths of Langevin diffusions. We use the entropy method to prove existence of an infinite-volume Gibbs point process and use cluster expansion tools to provide an explicit activity domain in which uniqueness holds.

Appeared in

  • Markov Process. Related Fields, 28 (2022), pp. 329--364.

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