Precise Asymptotics for the Parabolic Anderson Model with a Moving Catalyst or Trap

@article{Schnitzler2012PreciseAF,
  title={Precise Asymptotics for the Parabolic Anderson Model with a Moving Catalyst or Trap},
  author={Adrian Schnitzler and Tilman Wolff},
  journal={arXiv: Probability},
  year={2012},
  pages={69-89}
}
We consider the solution \(u: [0,\infty ) \times{\mathbb{Z}}^{d} \rightarrow[0,\infty )\) to the parabolic Anderson model, where the potential is given by \((t,x)\mapsto \gamma {\delta }_{{Y }_{t}}\left (x\right )\) with Y a simple symmetric random walk on \({\mathbb{Z}}^{d}\). Depending on the parameter γ∈[−∞,∞), the potential is interpreted as a randomly moving catalyst or trap. 
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We consider the parabolic Anderson model (PAM) which is given by the equation ∂u∕∂t=κΔu+ξu with \(u: \,{\mathbb{Z}}^{d} \times[0,\infty ) \rightarrow\mathbb{R}\), where κ∈[0,∞) is the diffusion
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We continue our study of the parabolic Anderson equation ∂u ∕ ∂t = κΔu + γξu for the space–time field \(u: \,{\mathbb{Z}}^{d} \times [0,\infty ) \rightarrow \mathbb{R}\), where κ ∈ [0, ∞) is the
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