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The parabolic Anderson problem is the Cauchy problem for the heat equation with random potential and localized initial condition. In this paper, we consider potentials which are constant in time and independent exponentially distributed in space. We study the growth rate of the total mass of the solution in terms of weak and almost sure limit theorems, and the spatial spread of the mass in terms of a scaling limit theorem. The latter result shows that in this case, just like in the case of heavy tailed potentials, the mass gets trapped in a single relevant island with high probability.
|Title of host publication||Probability in complex physical systems|
|Subtitle of host publication||In honour of Jürgen Gärtner and Erwin Bolthausen|
|Editors||J. D. Deuschel, Barbara Gentz , Wolfgang Konig , Max Von Reesse , Michael Scheutzow , Uwe Schmock|
|Place of Publication||Berlin|
|Publication status||Published - 2012|
|Name||Springer Proceedings in Mathematics|