The Discrete Gaussian model, II. Infinite-volume scaling limit at high temperature
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866929415242383360 |
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| author | Bauerschmidt, Roland Park, Jiwoon Rodriguez, Pierre-François |
| author_facet | Bauerschmidt, Roland Park, Jiwoon Rodriguez, Pierre-François |
| contents | The Discrete Gaussian model is the lattice Gaussian free field conditioned to be integer-valued. In two dimensions, at sufficiently high temperature, we show that the scaling limit of the infinite-volume gradient Gibbs state with zero mean is a multiple of the Gaussian free field.
This article is the second in a series on the Discrete Gaussian model, extending the methods of the first paper by the analysis of general external fields (rather than macroscopic test functions on the torus). As a byproduct, we also obtain a scaling limit for mesoscopic test functions on the torus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_02287 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The Discrete Gaussian model, II. Infinite-volume scaling limit at high temperature Bauerschmidt, Roland Park, Jiwoon Rodriguez, Pierre-François Probability Mathematical Physics 82B20, 82B28, 60G15, 60K35 (primary) The Discrete Gaussian model is the lattice Gaussian free field conditioned to be integer-valued. In two dimensions, at sufficiently high temperature, we show that the scaling limit of the infinite-volume gradient Gibbs state with zero mean is a multiple of the Gaussian free field. This article is the second in a series on the Discrete Gaussian model, extending the methods of the first paper by the analysis of general external fields (rather than macroscopic test functions on the torus). As a byproduct, we also obtain a scaling limit for mesoscopic test functions on the torus. |
| title | The Discrete Gaussian model, II. Infinite-volume scaling limit at high temperature |
| topic | Probability Mathematical Physics 82B20, 82B28, 60G15, 60K35 (primary) |
| url | https://arxiv.org/abs/2202.02287 |