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.
LanguageEnglish
Title of host publicationSurveys in Stochastic Processes
PublisherEuropean Mathematical Society
Pages67-85
Number of pages19
StatusPublished - 2011

Publication series

NameEMS Series of Congress Report
PublisherEuropean Mathematical Society

Fingerprint

Anderson Model
Irregular
Random Potential
Heavy Tails
Heat Equation
Identically distributed
Diffusion Process
Random Field
Cauchy Problem
Fluctuations
Model

Cite this

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.

The parabolic Anderson model with heavy-tailed potential. / Morters, Peter.

Surveys in Stochastic Processes. European Mathematical Society, 2011. p. 67-85 (EMS Series of Congress Report).

Research output: Chapter in Book/Report/Conference proceedingChapter

Morters, P 2011, The parabolic Anderson model with heavy-tailed potential. in Surveys in Stochastic Processes. EMS Series of Congress Report, European Mathematical Society, pp. 67-85.
Morters P. The parabolic Anderson model with heavy-tailed potential. In Surveys in Stochastic Processes. European Mathematical Society. 2011. p. 67-85. (EMS Series of Congress Report).
Morters, Peter. / The parabolic Anderson model with heavy-tailed potential. Surveys in Stochastic Processes. European Mathematical Society, 2011. pp. 67-85 (EMS Series of Congress Report).
@inbook{34d10c71fedc41809ab6876b66ef6f07,
title = "The parabolic Anderson model with heavy-tailed potential",
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.",
author = "Peter Morters",
year = "2011",
language = "English",
series = "EMS Series of Congress Report",
publisher = "European Mathematical Society",
pages = "67--85",
booktitle = "Surveys in Stochastic Processes",

}

TY - CHAP

T1 - The parabolic Anderson model with heavy-tailed potential

AU - Morters,Peter

PY - 2011

Y1 - 2011

N2 - 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.

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 - Chapter

T3 - EMS Series of Congress Report

SP - 67

EP - 85

BT - Surveys in Stochastic Processes

PB - European Mathematical Society

ER -