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Publication 16-CNA-016
Martin Hairer Gautam Iyer Leonid Koralov Alexei Novikov Zsolt Pajor-Gyulai Abstract: This paper studies the intermediate time behaviour of a small random perturbation of a periodic cellular
flow. Our main result shows that on time scales shorter than the diffusive time scale, the limiting behaviour
of trajectories that start close enough to cell boundaries is a fractional kinetic process: A Brownian motion
time changed by the local time of an independent Brownian motion. Our proof uses the Freidlin-Wentzell
framework, and the key step is to establish an analogous averaging principle on shorter time scales.As a consequence of our main theorem, we obtain a homogenization result for the associated advection diffusion equation. We show that on intermediate time scales the effective equation is a fractional time
PDE that arises in modelling anomalous diffusion.Get the paper in its entirety as 16-CNA-016.pdf |