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.
Author details: | Sylvie RoellyGND, W. M. Ruszel |
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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 |