The parabolic Anderson model with heavy-tailed potential

Peter Morters

Research output: Chapter in Book/Report/Conference proceedingChapter

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 languageEnglish
Title of host publicationSurveys in Stochastic Processes
PublisherEuropean Mathematical Society
Pages67-85
Number of pages19
Publication statusPublished - 2011

Publication series

NameEMS Series of Congress Report
PublisherEuropean Mathematical Society

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