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arXiv · 2511.15473

A Critical Drift-Diffusion Equation: Intermittent Behavior via Geometric Brownian Motion on $ \textbf{SL}(n)$

Peter S. Morfe·Felix Otto·Christian Wagner
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Abstract

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.

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Peter S. Morfe, Felix Otto, Christian Wagner. 2025-11-19. A Critical Drift-Diffusion Equation: Intermittent Behavior via Geometric Brownian Motion on $ \textbf{SL}(n)$. https://arxiv.org/abs/2511.15473

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