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Limit shapes for the dimer model

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arxiv 1712.08396 v1 pith:6CDXDB7N submitted 2017-12-22 math-ph math.MPmath.PR

Nikolai Kuchumov This is my paper · ORCID
classification math-phmath.MPmath.PR
keywords modelarbitrarydimerlimitperiodicbipartitecompactnessdomain
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We prove the existence of a limit shape for the dimer model on planar periodic bipartite graphs with an arbitrary fundamental domain and arbitrary periodic weights. This proof is based on a variational principle that uses the locality of the model and the compactness of the space of states.

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  1. Gaussian Free Field and Discrete Gaussians in Periodic Dimer Models

    math.PR 2025-02 conditional novelty 7.0 of 10

    Periodic Aztec diamond height fluctuations are shown to decompose into a Gaussian free field plus a discrete-Gaussian random harmonic component.

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