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

Autoren: Alexander Zass (2022)

We study a class of infinite-dimensional diffusions under Gibbsian interactions, in the context of marked point configurations: the starting points belong to ℝd, 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.

Zeitschrift:
Markov processes and random fields

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