The parabolic Anderson model with heavy-tailed potential

Peter Morters

The parabolic Anderson model with heavy-tailed potential

Peter Morters

Research output: Chapter or section in a book/report/conference proceeding › Book chapter

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	67-85
Number of pages	19
Publication status	Published - 2011

Publication series

Name	EMS Series of Congress Report
Publisher	European Mathematical Society

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

Cite this

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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.",

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AB - 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.

M3 - Book chapter

T3 - EMS Series of Congress Report

SP - 67

EP - 85

BT - Surveys in Stochastic Processes

PB - European Mathematical Society

ER -

The parabolic Anderson model with heavy-tailed potential

Abstract

Publication series

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INTERSECTION LOCAL TIMES AND STOCHASTIC PROCESSES IN RANDOM MEDIA

Cite this