Stochastic dynamics of fluctuations in classical continuous systems (Q5949552)

This work, like previous ones by the same authors and others, is devoted to the study of stochastic dynamics. The space of configurations is the space of locally finite subsets of a Euclidean space, where the elements of the subsets are interpreted as particles. One is given a potential which describes the interaction between particles; in the low activity high temperature regime, it is known that the Gibbs measure has good mixing properties. Here, the authors consider local observables on the space of configurations, and associate to them a notion of fluctuation which is a renormalised central limit with respect to the convergence to the Gibbs measure. Mathematically, they have to introduce a space of macroscopic fluctuations. This type of space has already been considered for lattice models, and is here constructed for the continuous case under study.