A new discrete Edwards model and a new polymer measure in two dimensions

The new discrete Edwards models in this paper are defined in terms of the so-called restricted intersection local times of the lattice random walk in two dimensions. We study the asymptotic behaviours of these new discrete Edwards models in the superrenormalizable cases. In particular, by approximating these models we can construct new polymer measures in two dimensions which are different from the original polymer measures obtained by approximating the original discrete Edwards models. The new discrete Edwards models can be thought of as zero-component lattice ω⁴-fields with different cutoffs in the free and interacting parts.