Dynamical interface above a hard wall and reflected SPDE on the half-line
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911136836747264 |
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| author | Faugère, Pierre Labbé, Cyril |
| author_facet | Faugère, Pierre Labbé, Cyril |
| contents | We consider a dynamical random interface on the infinite lattice $\mathbb{N}$ evolving according to a "corner flip" dynamic above a hard wall, with an additional pinning at the origin. We study the stationary fluctuations under a diffusive scaling and prove convergence in law towards the solution of an SPDE of Nualart-Pardoux's type, namely the Reflected Stochastic Heat Equation on the half-line. We also obtain that the law of the 3-dimensional Bessel process is an invariant measure for this SPDE. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_03328 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dynamical interface above a hard wall and reflected SPDE on the half-line Faugère, Pierre Labbé, Cyril Probability We consider a dynamical random interface on the infinite lattice $\mathbb{N}$ evolving according to a "corner flip" dynamic above a hard wall, with an additional pinning at the origin. We study the stationary fluctuations under a diffusive scaling and prove convergence in law towards the solution of an SPDE of Nualart-Pardoux's type, namely the Reflected Stochastic Heat Equation on the half-line. We also obtain that the law of the 3-dimensional Bessel process is an invariant measure for this SPDE. |
| title | Dynamical interface above a hard wall and reflected SPDE on the half-line |
| topic | Probability |
| url | https://arxiv.org/abs/2509.03328 |