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Abstract
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 language  English 

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 
Publisher  Springer 
Pages  247272 
Volume  11 
ISBN (Electronic)  9783642238116 
ISBN (Print)  9783642238109 
DOIs  
Publication status  Published  2012 
Publication series
Name  Springer Proceedings in Mathematics 

Volume  11 
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Dive into the research topics of 'A scaling limit theorem for the parabolic Anderson model with exponential potential'. Together they form a unique fingerprint.Projects
 1 Finished

INTERSECTION LOCAL TIMES AND STOCHASTIC PROCESSES IN RANDOM MEDIA
Morters, P.
Engineering and Physical Sciences Research Council
1/09/05 → 31/08/10
Project: Research council