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

  • 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.

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Metadaten
Author details:Sylvie RoellyGND, W. M. Ruszel
ISSN:1024-2953
Title of parent work (English):Markov processes and related fields
Publisher:Polymat
Place of publishing:Moscow
Publication type:Article
Language:English
Year of first publication:2014
Publication year:2014
Release date:2017/03/27
Tag:Girsanov formula; cluster expansion; infinite-dimensional diffusion; non-Markov drift; planar rotors; ultracontractivity
Volume:20
Issue:4
Number of pages:22
First page:653
Last Page:674
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Peer review:Referiert
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