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Abstract
The parabolic Anderson model is the Cauchy problem for the heat equation with random potential. It offers a case study for the effects that a random, or irregular, environment can have on a diffusion process. The main focus in the present survey is on phenomena that are due to a highly irregular potential, which we model by a spatially independent, identically distributed random field with heavy tails. Among the effects we discuss are random fluctuations in the growth of the total mass, localisation in the weak and almost sure sense, and ageing.
Original language  English 

Title of host publication  Surveys in Stochastic Processes 
Publisher  European Mathematical Society 
Pages  6785 
Number of pages  19 
Publication status  Published  2011 
Publication series
Name  EMS Series of Congress Report 

Publisher  European Mathematical Society 
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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