### Abstract

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

### Cite this

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

**A scaling limit theorem for the parabolic Anderson model with exponential potential.** / Lacoin, Hubert; Morters, Peter.

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

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

}

TY - CHAP

T1 - A scaling limit theorem for the parabolic Anderson model with exponential potential

AU - Lacoin, Hubert

AU - Morters, Peter

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

UR - http://dx.doi.org/10.1007/978-3-642-23811-6_10

U2 - 10.1007/978-3-642-23811-6_10

DO - 10.1007/978-3-642-23811-6_10

M3 - Chapter

SN - 9783642238109

VL - 11

T3 - Springer Proceedings in Mathematics

SP - 247

EP - 272

BT - Probability in complex physical systems

A2 - Deuschel, J. D.

A2 - Gentz , Barbara

A2 - Konig , Wolfgang

A2 - Von Reesse , Max

A2 - Scheutzow , Michael

A2 - Schmock , Uwe

PB - Springer

CY - Berlin

ER -