Second Order Asymptotics for the Hard Wall Probability of the 2D Harmonic Crystal
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917211406336000 |
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| author | Fels, Maximilian Louidor, Oren Wu, Tianqi |
| author_facet | Fels, Maximilian Louidor, Oren Wu, Tianqi |
| contents | We estimate the probability that the discrete Gaussian free field on a planar domain with Dirichlet boundary conditions stays positive in the bulk. Improving upon the result by Bolthausen, Deuschel and Giacomin from 2001, we derive the order of the subleading term of this probability when a sequence of discretized scale-ups of given domain and compactly included smooth bulk are considered. A main ingredient in the proof is the double exponential decay of the right tail of the centered minimum of the field in the bulk, conditioned on a certain weighted average of its values to be zero. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_13738 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Second Order Asymptotics for the Hard Wall Probability of the 2D Harmonic Crystal Fels, Maximilian Louidor, Oren Wu, Tianqi Probability 60G15, 82B41 We estimate the probability that the discrete Gaussian free field on a planar domain with Dirichlet boundary conditions stays positive in the bulk. Improving upon the result by Bolthausen, Deuschel and Giacomin from 2001, we derive the order of the subleading term of this probability when a sequence of discretized scale-ups of given domain and compactly included smooth bulk are considered. A main ingredient in the proof is the double exponential decay of the right tail of the centered minimum of the field in the bulk, conditioned on a certain weighted average of its values to be zero. |
| title | Second Order Asymptotics for the Hard Wall Probability of the 2D Harmonic Crystal |
| topic | Probability 60G15, 82B41 |
| url | https://arxiv.org/abs/2601.13738 |