8 papers
Diffuse Interface Energies with Microscopic Heterogeneities II: Rare Events
Peter S. Morfe, Christian Wagner
We analyze Allen-Cahn functionals with stationary ergodic coefficients in the regime where the length scale of the heterogeneities is much smaller (microscopic) than the interf…
Intermittency of geometric Brownian motion on
Sefika Kuzgun, Felix Otto, Christian Wagner
This short note is motivated by a recently discovered connection between a drift-diffusion process in -dimensional Euclidean space with a divergence-free drift sampled from a st…
A Critical Drift-Diffusion Equation: Intermittent Behavior via Geometric Brownian Motion on
Peter S. Morfe, Felix Otto, Christian Wagner
This paper concerns the so-called diffusion in the curl of the 2d Gaussian free field, and its generalization to higher dimensions , building on the scale-by-scale homoge…
On minimizing curves in a Brownian potential
Felix Otto, Matteo Palmieri, Christian Wagner
We study a -dimensional semi-discrete random variational problem that can be interpreted as the geometrically linearized version of the critical -dimensional random field…
A Critical Drift-Diffusion Equation: Connections to the Diffusion on
Peter Morfe, Felix Otto, Christian Wagner
In this note, we connect two seemingly unrelated objects: On the one hand is a two-dimensional drift-diffusion process with divergence-free and time-independent drift . The…
Diffuse Interface Energies with Microscopic Heterogeneities I: Homogenization
Peter S. Morfe, Christian Wagner
We analyze Allen-Cahn functionals with stationary ergodic coefficients in the regime where the length scale of the heterogeneities is much smaller (microscopic) than the interf…
A critical drift-diffusion equation: intermittent behavior
Felix Otto, Christian Wagner
We consider a drift-diffusion process with a time-independent and divergence-free random drift that is of white-noise character. We are interested in the critical case of two space…
The Gaussian free-field as a stream function: continuum version of the scale-by-scale homogenization result
Peter Morfe, Felix Otto, Christian Wagner
This note is about a drift-diffusion process with a time-independent, divergence-free drift , where is a smooth Gaussian field that decorrelates over large scales. In tw…