Propagation of Gibbsianness for infinite-dimensional diffusions with space-time interaction

S. Rœlly, W.M. Ruszel

Research output: Contribution to journalArticleScientificpeer-review

4 Citations (Scopus)

Abstract

We consider infinite-dimensional diffusions where the interaction between the coordinates has a finite extent both in space and time. In particular, it is not supposed to be smooth or Markov. The initial state of the system is Gibbs, given by a strong summable interaction. If the strongness of this initial interaction is lower than a suitable level, and if the dynamical interaction is bounded from above in a right way, we prove that the law of the diffusion at any time t is a Gibbs measure with absolutely summable interaction. The main tool is a cluster expansion in space uniformly in time of the Girsanov factor coming from the dynamics and exponential ergodicity of the free dynamics to an equilibrium product measure.
Original languageEnglish
Pages (from-to)653-674
Number of pages22
JournalMarkov Processes and Related Fields
Volume20
Issue number4
Publication statusPublished - 2014

Keywords

  • infinite-dimensional diffusion
  • cluster expansion
  • non-Markov drift
  • Girsanov formula
  • ultracontractivity
  • planar rotors

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