How the Unbounded Drift Shapes the Dirichlet Semigroups Behaviour of Non-Gaussian Gibbs Measures

We investigate the Dirichlet operator semigroups of non-Gaussian Gibbs measures on linear spin lattice systems. We prove that Dirichlet semigroups preserve spaces ofL2-differentiable functions. We show how the non-linearity and unboundedness of drift term in Dirichlet operator affects the structure of the spaces involved.