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

Hubert Lacoin, Peter Morters

Research output: Chapter in Book/Report/Conference proceedingChapter

5 Citations (Scopus)
80 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 languageEnglish
Title of host publicationProbability in complex physical systems
Subtitle of host publicationIn honour of Jürgen Gärtner and Erwin Bolthausen
EditorsJ. D. Deuschel, Barbara Gentz , Wolfgang Konig , Max Von Reesse , Michael Scheutzow , Uwe Schmock
Place of PublicationBerlin
PublisherSpringer
Pages247-272
Volume11
ISBN (Electronic)9783642238116
ISBN (Print)9783642238109
DOIs
Publication statusPublished - 2012

Publication series

NameSpringer Proceedings in Mathematics
Volume11

Fingerprint

Anderson Model
Scaling Limit
Limit Theorems
Almost Sure Limit Theorem
Random Potential
Heat Equation
Cauchy Problem
Initial conditions

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). 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.

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 in Book/Report/Conference proceedingChapter

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). https://doi.org/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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