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Limit shapes from harmonicity: dominos and the five vertex model

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arxiv 2310.06429 v2 pith:I5QUNC4R submitted 2023-10-10 math.PR

Richard Kenyon , István Prause This is my paper · ORCID
classification math.PR
keywords modellimitshapesvertexappropriateconstructdimerdiscuss
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abstract

We discuss how to construct limit shapes for the domino tiling model (square lattice dimer model) and $5$-vertex model, in appropriate polygonal domains. Our methods are based on the harmonic extension method of [R. Kenyon and I. Prause, Gradient variational problems in $\mathbb{R}^2$, Duke Math J. 2022].

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  1. Domino Tilings of the Aztec Diamond in Random Environment and Schur Generating Functions

    math.PR 2025-07 conditional novelty 7.0 of 10

    For Aztec diamond tilings with i.i.d. one-periodic edge weights, height function fluctuations are, in the critical regime, GFF plus independent Brownian motion, and in the fixed-variance regime, Brownian motion alone ...

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