Planar $3$-webs and the boundary measurement matrix

Richard Kenyon; Haolin Shi

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arXiv · 2312.14761

Planar $3$-webs and the boundary measurement matrix

Richard Kenyon·Haolin Shi

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Abstract

We compute connection probabilities for reduced $3$-webs in the triple-dimer model on circular planar graphs using the boundary measurement matrix (reduced Kasteleyn matrix). As one application we compute several "$\text{SL}_3$ generalizations'' of the Lindstr{\o}m-Gessel-Viennot theorem, for "parallel" webs and for honeycomb webs. We also apply our results to the scaling limit of the dimer model in a planar domain, giving conformally invariant expressions for reduced web probabilities.

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Richard Kenyon, Haolin Shi. 2023-12-22. Planar $3$-webs and the boundary measurement matrix. https://arxiv.org/abs/2312.14761

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