Local Statistics of the M_n-Dimer Model

2025/08/26 by Anderson, Nickolas, Elkin, Moriah, Kelley, Elizabeth +2 · 2 citations
#05C70 #82B20 #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2508.19224

Abstract

The classical dimer model is concerned with the (weighted) enumeration of perfect matchings of a graph. An n-dimer cover is a multiset of edges that can be realized as the disjoint union of n individual matchings. For a probability measure recently defined by Douglas, Kenyon, and Shi, which we call the M_n-dimer model, we study random n-dimer covers on bipartite graphs with matrix edge weights and produce formulas for local edge statistics and correlations. We also classify local moves that can be used to simplify the analysis of such graphs.

Citations

• Higher-rank dimer models
• Dimers, webs, and local systems
• Farey boat I. Continued fractions and triangulations, modular group and polygon dissections
• From dimers to webs
• Dimers and cluster integrable systems
• Lectures on Dimers
• Total positivity, Grassmannians, and networks
• The combinatorics of frieze patterns and Markoff numbers
• Generalized domino-shuffling
• Generalized domino-shuffling
• Quasideterminants, I

Cited by

• q-rationals and dimers
• A quantum N-dimer model

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• Asymptotics of the partial n-fold dimer model
• The multinomial dimer model
• Local Statistics and Shuffling for Dimers on a Square-Hexagon Lattice
• Edge Effects on Local Statistics in Lattice Dimers: A Study of the Aztec Diamond (Finite Case)
• Lectures on Dimers