Propagation of Gibbsianness for infinite-dimensional diffusions with space-time interaction
Mathematical Physics
2013-12-03 v1 math.MP
Probability
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.
Keywords
Cite
@article{arxiv.1312.0394,
title = {Propagation of Gibbsianness for infinite-dimensional diffusions with space-time interaction},
author = {Sylvie Roelly and Wioletta Ruszel},
journal= {arXiv preprint arXiv:1312.0394},
year = {2013}
}
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