We consider a random walk among time-dependent random weights. In the
talk, I will discuss recent progress on the understanding of the
long-times behaviour of such random walks. A particular emphasis will
be on the results and methods that can be used to prove second space
derivatives of the annealed transition density.
This is work in progress jointly with Jean-Dominique Deuschel (TU
Berlin) and Takashi Kumagai (RIMS Kyoto).