Edwards-Wilkinson limit for a stochastic advection-diffusion PDE
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908599715889152 |
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| author | Kotitsas, Sotirios Luo, Dejun Maurelli, Mario |
| author_facet | Kotitsas, Sotirios Luo, Dejun Maurelli, Mario |
| contents | We consider a diffusion in a Gaussian random environment that is white in time and study the large-scale behavior of the quenched density with respect to the Lebesgue measure. We show that under diffusive rescaling, the fluctuations of the density converge to a Gaussian limit, described by an additive stochastic heat equation. In the case where the environment is divergence-free, our result can be interpreted as computing the scaling limit of the first-order correction to the quenched Central Limit Theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_07956 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Edwards-Wilkinson limit for a stochastic advection-diffusion PDE Kotitsas, Sotirios Luo, Dejun Maurelli, Mario Probability We consider a diffusion in a Gaussian random environment that is white in time and study the large-scale behavior of the quenched density with respect to the Lebesgue measure. We show that under diffusive rescaling, the fluctuations of the density converge to a Gaussian limit, described by an additive stochastic heat equation. In the case where the environment is divergence-free, our result can be interpreted as computing the scaling limit of the first-order correction to the quenched Central Limit Theorem. |
| title | Edwards-Wilkinson limit for a stochastic advection-diffusion PDE |
| topic | Probability |
| url | https://arxiv.org/abs/2509.07956 |