Projects per year

### Abstract

The parabolic Anderson problem is the Cauchy problem for the heat equation with random potential and localized initial condition. In this paper, we consider potentials which are constant in time and independent exponentially distributed in space. We study the growth rate of the total mass of the solution in terms of weak and almost sure limit theorems, and the spatial spread of the mass in terms of a scaling limit theorem. The latter result shows that in this case, just like in the case of heavy tailed potentials, the mass gets trapped in a single relevant island with high probability.

Original language | English |
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Title of host publication | Probability in complex physical systems |

Subtitle of host publication | In honour of Jürgen Gärtner and Erwin Bolthausen |

Editors | J. D. Deuschel, Barbara Gentz , Wolfgang Konig , Max Von Reesse , Michael Scheutzow , Uwe Schmock |

Place of Publication | Berlin |

Publisher | Springer |

Pages | 247-272 |

Volume | 11 |

ISBN (Electronic) | 9783642238116 |

ISBN (Print) | 9783642238109 |

DOIs | |

Publication status | Published - 2012 |

### Publication series

Name | Springer Proceedings in Mathematics |
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Volume | 11 |

## Fingerprint Dive into the research topics of 'A scaling limit theorem for the parabolic Anderson model with exponential 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

Lacoin, H., & Morters, P. (2012). A scaling limit theorem for the parabolic Anderson model with exponential potential. In J. D. Deuschel, B. Gentz , W. Konig , M. Von Reesse , M. Scheutzow , & U. Schmock (Eds.),

*Probability in complex physical systems: In honour of Jürgen Gärtner and Erwin Bolthausen*(Vol. 11, pp. 247-272). (Springer Proceedings in Mathematics; Vol. 11). Springer. https://doi.org/10.1007/978-3-642-23811-6_10