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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.08771 |
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| _version_ | 1866911310400192512 |
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| author | Gonçalves, Patrícia Hairer, Martin Ricciuti, Maria Chiara |
| author_facet | Gonçalves, Patrícia Hairer, Martin Ricciuti, Maria Chiara |
| contents | We consider a random interface model on the discrete torus with $2n$ sites, obtained from the classical corner flip dynamics but with a weak global perturbation, namely an asymmetry of order $n^{-γ}$ of the direction of growth that switches direction based on the sign of the total area under the interface. The slopes of this model can be viewed as a non-simple exclusion process at half filling with globally dependent rates. We show that, for $γ=1$, the hydrodynamic equation of the empirical density is given by a time concatenation of the viscous Burgers equation and the heat equation. Moreover, for $n$ prime and $γ>\frac{6}{7}$, we establish convergence in law of the equilibrium fluctuations to an infinite-dimensional Ornstein-Uhlenbeck process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_08771 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Scaling Limits of a Weakly Perturbed Random Interface Model Gonçalves, Patrícia Hairer, Martin Ricciuti, Maria Chiara Probability We consider a random interface model on the discrete torus with $2n$ sites, obtained from the classical corner flip dynamics but with a weak global perturbation, namely an asymmetry of order $n^{-γ}$ of the direction of growth that switches direction based on the sign of the total area under the interface. The slopes of this model can be viewed as a non-simple exclusion process at half filling with globally dependent rates. We show that, for $γ=1$, the hydrodynamic equation of the empirical density is given by a time concatenation of the viscous Burgers equation and the heat equation. Moreover, for $n$ prime and $γ>\frac{6}{7}$, we establish convergence in law of the equilibrium fluctuations to an infinite-dimensional Ornstein-Uhlenbeck process. |
| title | Scaling Limits of a Weakly Perturbed Random Interface Model |
| topic | Probability |
| url | https://arxiv.org/abs/2512.08771 |