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The multinomial dimer model
Richard Kenyon, Catherine Wolfram
https://arxiv.org/abs/2506.12171 https://arxiv.org/pdf/2506.12171

The multinomial dimer model
An $N$-dimer cover of a graph is a collection of edges (with multiplicity) such that each vertex is contained in exactly $N$ edges in the collection. The multinomial dimer model is a natural probability measure on $N$-dimer covers. We study the behavior of these measures on periodic bipartite graphs in ${\mathbb R}^d$, in the scaling limit as the multiplicity $N$ and then the size of the graph go to infinity. In this iterated limit, we prove a large deviation principle, where the rate functio…