Speaker
Description
The course will discuss at least two of the following three topics.
1.
Random walks and diffusions in divergence-free random drift fields.
Motivation, examples, main questions.
Diffusive limit (CLT) and homogenisation under H_{-1} and ellipticity. (In probability and quenched, w.r.t. the environment)
Relaxing the ellipticity condition. Motivation (why care?). Diffusive limit and homogenisation (CLT) (in probability w.r.t. the environment).
Anomalous super-diffusion when H_{-1} fails - examples.
Open problems and questions.
2.
Random walks and diffusions with path-wise self-repellence.
Motivation, examples, main questions.
Super-diffusion in 1 and 2 dimensions.
Diffusive limits (CLT) in 3 dimensions.
Open problems and questions.
3.
Diffusive limit (invariance principle) for the random Lorentz gas beyond the kinetic time scales.
Boltzmann-Grad (low density) approximation on longer-than-kinetic time scales.
Weak coupling approximation on longer-than-kinetic time scales.
Open problems and questions.
