Uniqueness of diffusion generators for two types of particle systems with singular interactions (Q1883235)

Two specific models of stochastic particle systems in \(\mathbb R^d\) are studied. The first model is connected with a particle performing in a random motion and interacting with randomly distributed impurities, and the second describes a system with \(N\) particles, interacting via a singular pair potential. The \(L^1\)- and \(L^2\)-uniqueness w.r.t. the underlying symmetrizing measures of these two models are proved, which, in particular, implies the non-explosion of these particle systems.