Projects per year

### 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 |
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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 |

## Fingerprint Dive into the research topics of 'The parabolic Anderson model with heavy-tailed potential'. Together they form a unique fingerprint.

## Projects

- 1 Finished

### INTERSECTION LOCAL TIMES AND STOCHASTIC PROCESSES IN RANDOM MEDIA

Morters, P.

Engineering and Physical Sciences Research Council

1/09/05 → 31/08/10

Project: Research council

## 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.