Astral diffusion as a limit process for symmetric random walk in a high contrast periodic medium
A talk in the Oberseminar Analysis series by Elena Zhizhina from Moskau
The asymptotic properties of a symmetric random walk in a high contrast periodic medium on the lattice are considered.
We show that under proper diffusive scaling the random walk exhibits a non-standard limit behaviour.
In addition to the coordinate of the random walk in $\mathbb Z^d$ we introduce an extra variable that characterizes
the position of the random walk in the period and show that this two-component process
converges in law to a limit Markov process.
The components of the limit process are mutually coupled, thus we cannot expect that the limit behaviour of the coordinate
process is Markov. (This is a joint work with Andrey Piatnitski)
Within the CRC this talk is associated to the project(s): A2