Short-time Gibbsianness for Infinite-dimensional Diffusions with Space-Time Interaction
Probability
2015-05-14 v1 Mathematical Physics
math.MP
Abstract
We consider a class of infinite-dimensional diffusions where the interaction between the components is both spatial and temporal. We start the system from a Gibbs measure with finite-range uniformly bounded interaction. Under suitable conditions on the drift, we prove that there exists such that the distribution at time is a Gibbs measure with absolutely summable interaction. The main tool is a cluster expansion of both the initial interaction and certain time-reversed Girsanov factors coming from the dynamics.
Cite
@article{arxiv.0909.4640,
title = {Short-time Gibbsianness for Infinite-dimensional Diffusions with Space-Time Interaction},
author = {F. Redig and S. Roelly and W. Ruszel},
journal= {arXiv preprint arXiv:0909.4640},
year = {2015}
}