The Airy line ensemble at the rough-smooth boundary
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866914357877669888 |
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| author | Chhita, Sunil Dauvergne, Duncan Finn, Thomas |
| author_facet | Chhita, Sunil Dauvergne, Duncan Finn, Thomas |
| contents | We study the rough-smooth boundary in the two-periodic Aztec diamond, a random domino tiling model exhibiting three types of macroscopic regions. We show that the height function at this boundary converges to an independent sum of an Airy surface and an i.i.d. noise field with fluctuations governed by the full-plane smooth phase. Going further, we prove convergence of a family of Temperleyan backbone paths to the Airy line ensemble. This gives the first convergence result for a family of undirected paths converging to the Airy line ensemble, as well as Airy convergence at a noisy boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_24063 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Airy line ensemble at the rough-smooth boundary Chhita, Sunil Dauvergne, Duncan Finn, Thomas Probability Mathematical Physics We study the rough-smooth boundary in the two-periodic Aztec diamond, a random domino tiling model exhibiting three types of macroscopic regions. We show that the height function at this boundary converges to an independent sum of an Airy surface and an i.i.d. noise field with fluctuations governed by the full-plane smooth phase. Going further, we prove convergence of a family of Temperleyan backbone paths to the Airy line ensemble. This gives the first convergence result for a family of undirected paths converging to the Airy line ensemble, as well as Airy convergence at a noisy boundary. |
| title | The Airy line ensemble at the rough-smooth boundary |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2602.24063 |