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

@article{Hofstad2008WeakAA,
title={Weak and almost sure limits for the parabolic Anderson model with heavy tailed potentials},
author={Remco van der Hofstad and Peter Morters and Nadia Sidorovatsup},
journal={Annals of Applied Probability},
year={2008},
volume={18},
pages={2450-2494}
}
• Published 21 June 2006
• Mathematics
• Annals of Applied Probability
We study the parabolic Anderson problem, that is, the heat equation partial derivative(t)u = Delta u + xi u on (0,infinity) x Z(d) with independent identically distributed random potential {xi(Z): Z is an element of Z(d)) and localized initial condition u(0, x) = 1(0)(x). Our interest is in the long-term behavior of the random total mass U(t) = Sigma(z) u (t, z) of the unique nonnegative solution in the case that the distribution of xi(0) is heavy tailed. For this, we study two paradigm cases…

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