Invariant measures for linear infinite particle systems with values in \([0,\infty)^ S\).
For the linear infinite particle systems with values in \([0,\infty)^ S\) whose transition rates are translation invariant, the set (\({\mathcal P}\cap {\mathcal S})_ e\) of extremal invariant and translation invariant probability measures was known. We prove that under additional assumptions on the transition rates (including the recurrence of a transition probability associated to the process), \({\mathcal P}_ e=({\mathcal P}\cap {\mathcal S})_ e.\) We apply this result to some examples, and we finally obtain \({\mathcal P}_ e\) in a simple way for the symmetric simple exclusion process in the irreducible and recurrent case.
extremal invariant and translation invariant probability measures
scientific article; zbMATH DE number 4074161