Random graph approach to Gibbs processes with pair interaction
A translation invariant Gibbs point process for a pair potential of a special type is constructed. The distribution of this process is obtained as the equilibrium distribution of a Markov chain of point processes in \({\mathbb{R}}^ d\) which are represented as a sequence of subsets of the set of vertices of a special random graph. This embedding permits to analyse Markov chain as well as to suggest a stochastic construction of the equilibrium. The constructions are carried out under the condition of ergodicity of the chain given in terms of the ``absence of percolation'' in the graph.
Markov chain imbedding in a random graph
translation invariant Gibbs point process
equilibrium distribution of a Markov chain
scientific article; zbMATH DE number 4199174