Weak and almost sure limits for the parabolic Anderson model with heavy tailed potentials

@inproceedings{Hofstad2006WeakAA,
  title={Weak and almost sure limits for the parabolic Anderson model with heavy tailed potentials},
  author={Remco van der Hofstad and Peter M{\"o}rters and Nadia Sidorova},
  year={2006}
}
We study the parabolic Anderson problem, that is, the heat equation ∂tu = u+ ξu on (0,∞)×Zd with independent identically distributed random potential {ξ(z) : z ∈ Zd } and localized initial condition u(0, x) = 10(x). Our interest is in the long-term behavior of the random total mass U(t) = ∑ z u(t, z) of the unique nonnegative solution in the case that the… CONTINUE READING