Timo Schlüter - Limit theorems for a random walk on oriented percolation
|Dates:||15 December 2021|
|Times:||15:00 - 16:00|
|What is it:||Seminar|
|Organiser:||Department of Mathematics|
Timo Schlüter (University of Basel) will speak in the Probability seminar.
We consider a directed random walk $X=(X_n)_n$ in a random environment on $\Z^d$. The environment is given by the backbone of an oriented percolation cluster. We show the existence of a measure $Q$ that is absolutely continuous with respect to the original measure $\bP$ and invariant with respect to the point of view of the particle. Furthermore we prove a quenched local limit theorem using the Radon-Nikodym derivative obtained from $Q$ with respect to $\bP$ as a suitable prefactor.
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