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arXiv · 2205.05139

Dimers, webs, and local systems

Daniel C. Douglas·Richard Kenyon·Haolin Shi
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Abstract

For a planar bipartite graph $\mathcal G$ equipped with a $\mathrm{SL}_n$-local system, we show that the determinant of the associated Kasteleyn matrix counts "$n$-multiwebs" (generalizations of $n$-webs) in $\mathcal G$, weighted by their web-traces. We use this fact to study random $n$-multiwebs in graphs on some simple surfaces.

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Daniel C. Douglas, Richard Kenyon, Haolin Shi. 2023-12-18. Dimers, webs, and local systems. https://arxiv.org/abs/2205.05139

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