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  - 
TY  - JOUR
A1  - Houdebert, Pierre
A1  - Zass, Alexander
T1  - An explicit Dobrushin uniqueness region for Gibbs point processes with repulsive interactions
JF  - Journal of applied probability / Applied Probability Trust
N2  - We present a uniqueness result for Gibbs point processes with interactions that come from a non-negative pair potential; in particular, we provide an explicit uniqueness region in terms of activity z and inverse temperature beta. The technique used relies on applying to the continuous setting the classical Dobrushin criterion. We also present a comparison to the two other uniqueness methods of cluster expansion and disagreement percolation, which can also be applied for this type of interaction.
KW  - Gibbs point process
KW  - DLR equations
KW  - uniqueness
KW  - Dobrushin criterion;
KW  - cluster expansion
KW  - disagreement percolation
Y1  - 2022
U6  - https://doi.org/10.1017/jpr.2021.70
SN  - 0021-9002
SN  - 1475-6072
VL  - 59
IS  - 2
SP  - 541
EP  - 555
PB  - Cambridge Univ. Press
CY  - Cambridge
ER  -