PUB - Publikationen an der Universität Bielefeld

A stochastic dynamics (X(t))(t >= 0) of a classical continuous system is a stochastic process which takes values in the space Gamma of all locally finite subsets (configurations) in R-d and which has a Gibbs measure mu as an invariant measure. We assume that It corresponds to a symmetric pair potential phi(x - y). An important class of stochastic dynamics of a classical continuous system is formed by diffusions. Till now, only one type of such dynamics the so-called gradient stochastic dynamics, or interacting Brownian particles-has been investigated. By using the theory of Dirichlet forms from [27], we construct and investigate a new type of stochastic dynamics, which we call infinite interacting diffusion particles. We introduce a Dirichlet form E-mu(Gamma) on L-2(Gamma;mu) and under general conditions on the potential phi, prove its closability. For a potential phi having a "weak" singularity at zero, we also write down an explicit form of the generator of E-mu(Gamma) on the set of smooth cylinder functions. We then show that, for any Dirichlct form E-mu(Gamma), there exists a diffusion process that is properly associated with it. Finally, in a way parallel to [17], we study a scaling limit of interacting diffusions in terms of convergence of the corresponding Dirichlet forms, and we also show that these scaled processes are tight in C([0, infinity), D'), where D' is the dual space of D : = C-0(infinity) (R-d).