Gaussian Free Field and Discrete Gaussians in Periodic Dimer Models

Tomas Berggren; Matthew Nicoletti

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arXiv · 2502.07241

Gaussian Free Field and Discrete Gaussians in Periodic Dimer Models

Tomas Berggren·Matthew Nicoletti

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Abstract

We analyze height fluctuations in Aztec diamond dimer models with nearly arbitrary periodic edge weights. We show that the centered height function approximates the sum of two independent components: a Gaussian free field on the multiply connected liquid region and a harmonic function with random liquid-gas boundary values. The boundary values are jointly distributed as a discrete Gaussian random vector. This discrete Gaussian distribution maintains a quasi-periodic dependence on $N$, a phenomenon also observed in multi-cut random matrix models.

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BibTeX RIS

Tomas Berggren, Matthew Nicoletti. 2025-02-11. Gaussian Free Field and Discrete Gaussians in Periodic Dimer Models. https://arxiv.org/abs/2502.07241

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