Nesting of double-dimer loops: local fluctuations and convergence to the nesting field of CLE(4)
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909447568228352 |
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| author | Basok, Mikhail Izyurov, Konstantin |
| author_facet | Basok, Mikhail Izyurov, Konstantin |
| contents | We consider the double-dimer model in the upper-half plane discretized by the square lattice with mesh size $δ$. For each point $x$ in the upper half-plane, we consider the random variable $N_δ(x)$ given by the number of the double-dimer loops surrounding this point. We prove that the normalized fluctuations of $N_δ(x)$ for a fixed $x$ are asymptotically Gaussian as $δ\to 0+$. Further, we prove that the double-dimer nesting field $N_δ(\cdot) - \mathbb{E}\, N_δ(\cdot)$, viewed as a random distribution in the upper half-plane, converges as $δ\to 0+$ to the nesting field of CLE(4) constructed by Miller, Watson and Wilson. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_01574 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nesting of double-dimer loops: local fluctuations and convergence to the nesting field of CLE(4) Basok, Mikhail Izyurov, Konstantin Mathematical Physics Probability We consider the double-dimer model in the upper-half plane discretized by the square lattice with mesh size $δ$. For each point $x$ in the upper half-plane, we consider the random variable $N_δ(x)$ given by the number of the double-dimer loops surrounding this point. We prove that the normalized fluctuations of $N_δ(x)$ for a fixed $x$ are asymptotically Gaussian as $δ\to 0+$. Further, we prove that the double-dimer nesting field $N_δ(\cdot) - \mathbb{E}\, N_δ(\cdot)$, viewed as a random distribution in the upper half-plane, converges as $δ\to 0+$ to the nesting field of CLE(4) constructed by Miller, Watson and Wilson. |
| title | Nesting of double-dimer loops: local fluctuations and convergence to the nesting field of CLE(4) |
| topic | Mathematical Physics Probability |
| url | https://arxiv.org/abs/2501.01574 |