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The parabolic Anderson model with heavy-tailed potential


Reference:

Morters, P., 2011. The parabolic Anderson model with heavy-tailed potential. In: Surveys in Stochastic Processes. European Mathematical Society, pp. 67-85. (EMS Series of Congress Report)

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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.

Details

Item Type Book Sections
CreatorsMorters, P.
DepartmentsFaculty of Science > Mathematical Sciences
Research CentresBath Institute for Complex Systems (BICS)
StatusPublished
ID Code26587

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