Asymptotics of the partial $n$-fold dimer model

Abstract

We study a model of colored multiwebs, which generalizes the dimer model to allow each vertex to be adjacent to \(n_v\) edges. These objects can be formulated as a random tiling of a graph with partial dimer covers. We examine the case of a cycle graph, and in particular we describe the local correlations of tiles in this setting.

14 pages, 3 figures. Final version to appear in Electron. Commun. Probab