Universite ́ de Valenciennes et du Hainaut-Cambrésis

We analyse different Gibbsian properties of interactive Brownian diffusions X indexed by the lattice Zd: X = (Xi(t), i ∈ Zd, t ∈ [0, T], 0 < T < +∞). In a first part, these processes are characterized as Gibbs states on path spaces of the form C([0, T],R)Zd. In a second part, we study the Gibbsian character on RZd of νt, the law at time t of the infinite-dimensional diffusion X(t), when the initial law ν = ν0 is Gibbsian