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arXiv · 2501.01574

Nesting of double-dimer loops: local fluctuations and convergence to the nesting field of CLE(4)

Mikhail Basok·Konstantin Izyurov
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Abstract

We consider the double-dimer model in the upper-half plane discretized by the square lattice with mesh size $\delta$. For each point $x$ in the upper half-plane, we consider the random variable $N_\delta(x)$ given by the number of the double-dimer loops surrounding this point. We prove that the normalized fluctuations of $N_\delta(x)$ for a fixed $x$ are asymptotically Gaussian as $\delta\to 0+$. Further, we prove that the double-dimer nesting field $N_\delta(\cdot) - \mathbb{E}\, N_\delta(\cdot)$, viewed as a random distribution in the upper half-plane, converges as $\delta\to 0+$ to the nesting field of CLE(4) constructed by Miller, Watson and Wilson.

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Mikhail Basok, Konstantin Izyurov. 2025-01-02. Nesting of double-dimer loops: local fluctuations and convergence to the nesting field of CLE(4). https://arxiv.org/abs/2501.01574

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