TY  - JOUR
A1  - Roelly, Sylvie
A1  - Ruszel, W. M.
T1  - Propagation of gibbsianness for infinite-dimensional diffusions with space-time interaction
JF  - Markov processes and related fields
N2  - 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.
KW  - infinite-dimensional diffusion
KW  - cluster expansion
KW  - non-Markov drift
KW  - Girsanov formula
KW  - ultracontractivity
KW  - planar rotors
Y1  - 2014
SN  - 1024-2953
VL  - 20
IS  - 4
SP  - 653
EP  - 674
PB  - Polymat
CY  - Moscow
ER  -