A Critical Drift-Diffusion Equation: Intermittent Behavior via Geometric Brownian Motion on $ \textbf{SL}(n)$
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917092701241344 |
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| author | Morfe, Peter S. Otto, Felix Wagner, Christian |
| author_facet | Morfe, Peter S. Otto, Felix Wagner, Christian |
| contents | This paper concerns the so-called diffusion in the curl of the 2d Gaussian free field, and its generalization to higher dimensions $n \geq 2$, building on the scale-by-scale homogenization approach developed recently by Chatzigeorgiou, Morfe, Otto, and Wang [13]. It begins by reformulating the approximation scheme of that work in terms of SDEs in the length scale $L$. This exposes an unexpected connection with a certain geometric Brownian motion on the special linear group $\textbf{SL}(n)$. The analysis of this process sheds light on the original problem, particularly as it pertains to intermittent behavior exhibited by the (averaged) Lagrangian coordinate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_15473 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Critical Drift-Diffusion Equation: Intermittent Behavior via Geometric Brownian Motion on $ \textbf{SL}(n)$ Morfe, Peter S. Otto, Felix Wagner, Christian Probability Analysis of PDEs This paper concerns the so-called diffusion in the curl of the 2d Gaussian free field, and its generalization to higher dimensions $n \geq 2$, building on the scale-by-scale homogenization approach developed recently by Chatzigeorgiou, Morfe, Otto, and Wang [13]. It begins by reformulating the approximation scheme of that work in terms of SDEs in the length scale $L$. This exposes an unexpected connection with a certain geometric Brownian motion on the special linear group $\textbf{SL}(n)$. The analysis of this process sheds light on the original problem, particularly as it pertains to intermittent behavior exhibited by the (averaged) Lagrangian coordinate. |
| title | A Critical Drift-Diffusion Equation: Intermittent Behavior via Geometric Brownian Motion on $ \textbf{SL}(n)$ |
| topic | Probability Analysis of PDEs |
| url | https://arxiv.org/abs/2511.15473 |