Asymptotics of the partial $n$-fold dimer model

TL;DR

This paper investigates the asymptotic behavior of a generalized dimer model on cycle graphs, focusing on local tile correlations in a colored multiweb framework, extending classical dimer theory.

Contribution

It introduces a generalized multiweb dimer model allowing multiple edges per vertex and analyzes local correlations specifically on cycle graphs.

Findings

Derived asymptotic properties of the multiweb dimer model.

Characterized local tile correlations in cycle graphs.

Extended classical dimer results to colored multiwebs.

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.