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

Hubert Lacoin; Peter Morters

doi:10.1007/978-3-642-23811-6_10

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

Hubert Lacoin, Peter Morters

Research output: Chapter or section in a book/report/conference proceeding › Book chapter

9 Citations (SciVal)

168 Downloads (Pure)

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
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	https://doi.org/10.1007/978-3-642-23811-6_10
Publication status	Published - 2012

Publication series

Name	Springer Proceedings in Mathematics
Volume	11

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

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The original publication is available at www.springerlink.com
Accepted author manuscript, 163 KB

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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

A scaling limit theorem for the parabolic Anderson model with exponential potential. / Lacoin, Hubert; Morters, Peter.
Probability in complex physical systems: In honour of Jürgen Gärtner and Erwin Bolthausen. ed. / J. D. Deuschel; Barbara Gentz ; Wolfgang Konig ; Max Von Reesse ; Michael Scheutzow ; Uwe Schmock . Vol. 11 Berlin: Springer, 2012. p. 247-272 (Springer Proceedings in Mathematics; Vol. 11).

Research output: Chapter or section in a book/report/conference proceeding › Book chapter

Lacoin, H & Morters, P 2012, A scaling limit theorem for the parabolic Anderson model with exponential potential. in JD 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, Springer Proceedings in Mathematics, vol. 11, Springer, Berlin, pp. 247-272. https://doi.org/10.1007/978-3-642-23811-6_10

Lacoin H, Morters P. A scaling limit theorem for the parabolic Anderson model with exponential potential. In Deuschel JD, Gentz B, Konig W, Von Reesse M, Scheutzow M, Schmock U, editors, Probability in complex physical systems: In honour of Jürgen Gärtner and Erwin Bolthausen. Vol. 11. Berlin: Springer. 2012. p. 247-272. (Springer Proceedings in Mathematics). doi: 10.1007/978-3-642-23811-6_10

Lacoin, Hubert ; Morters, Peter. / A scaling limit theorem for the parabolic Anderson model with exponential potential. Probability in complex physical systems: In honour of Jürgen Gärtner and Erwin Bolthausen. editor / J. D. Deuschel ; Barbara Gentz ; Wolfgang Konig ; Max Von Reesse ; Michael Scheutzow ; Uwe Schmock . Vol. 11 Berlin : Springer, 2012. pp. 247-272 (Springer Proceedings in Mathematics).

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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.

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

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INTERSECTION LOCAL TIMES AND STOCHASTIC PROCESSES IN RANDOM MEDIA

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

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INTERSECTION LOCAL TIMES AND STOCHASTIC PROCESSES IN RANDOM MEDIA

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