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Abstract
The parabolic Anderson model is the Cauchy problem for the heat equation with a random potential. We consider this model in a setting which is continuous in time and discrete in space, and focus on timeconstant, independent and identically distributed potentials with polynomial tails at infinity. We are concerned with the longterm temporal dynamics of this system. Our main result is that the periods, in which the profile of the solutions remains nearly constant, are increasing linearly over time, a phenomenon known as ageing. We describe this phenomenon in the weak sense, by looking at the asymptotic probability of a change in a given time window, and in the strong sense, by identifying the almost sure upper envelope for the process of the time remaining until the next change of profile. We also prove functional scaling limit theorems for profile and growth rate of the solution of the parabolic Anderson model.
Original language  English 

Pages (fromto)  9691000 
Number of pages  32 
Journal  Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 
Volume  47 
Issue number  4 
DOIs  
Publication status  Published  2011 
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 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