### Abstract

Original language | English |
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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 |
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Publisher | European Mathematical Society |

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### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Surveys in Stochastic Processes.*EMS Series of Congress Report, European Mathematical Society, pp. 67-85.

}

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 -