Canonical Gibbs measures DLR equation Gibbs measure Gibbs’s measure as a solution to the Dobrushin-Lanford-Ruelle equation Hamiltonian Interacting particle systems Local Gibbs specification Local Hamiltonian and partition functions for a positive Newton series Pair potential Poisson measure Radon-Nikodym derivatives Vector valued Radon measures Wick ordering bounded and measurable pair potential canonical commutation relations configuration spaces diffeomorphism groups falling factorials marked Poisson measures quasi-invariant measure spatial combinatorics symmetric tempered Gibbs measures