Annealed Asymptotics for the Parabolic Anderson Model with a Moving Catalyst

@inproceedings{Grtner2005AnnealedAF,
  title={Annealed Asymptotics for the Parabolic Anderson Model with a Moving Catalyst},
  author={J{\"u}rgen G{\"a}rtner and Markus Heydenreich},
  year={2005}
}
This paper deals with the solution u to the parabolic Anderson equation ∂u/∂t = κ∆u+ξu on the lattice Zd. We consider the case where the potential ξ is time-dependent and has the form ξ(t, x) = δ0(x − Yt) with Yt being a simple random walk with jump rate 2d̺. The solution u may be interpreted as the concentration of a reactant under the influence of a single catalyst particle Yt. In the first part of the paper we show that the moment Lyapunov exponents coincide with the upper boundary of the… CONTINUE READING