A scaling limit theorem for the parabolic Anderson model with exponential potential

Hubert Lacoin, Peter Morters

Research output: Chapter or section in a book/report/conference proceedingChapter or section

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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.
Original languageEnglish
Title of host publicationProbability in complex physical systems
Subtitle of host publicationIn honour of Jürgen Gärtner and Erwin Bolthausen
EditorsJ. D. Deuschel, Barbara Gentz , Wolfgang Konig , Max Von Reesse , Michael Scheutzow , Uwe Schmock
Place of PublicationBerlin
ISBN (Electronic)9783642238116
ISBN (Print)9783642238109
Publication statusPublished - 2012

Publication series

NameSpringer Proceedings in Mathematics


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