Very Strong Disorder for the Parabolic Anderson model in low dimensions

Abstract : We study the free energy of the Parabolic Anderson Model, a time-continuous model of directed polymers in random environment. We prove that in dimension 1 and 2, the free energy is always negative, meaning that very strong disorder always holds. The result for discrete polymers in dimension two, as well as better bounds on the free energy on dimension 1, were first obtained by Hubert Lacoin, and the goal of this paper is to adapt his proof to the Anderson Parabolic Model.
Type de document :
Pré-publication, Document de travail
2012
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https://hal.archives-ouvertes.fr/hal-00766752
Contributeur : Pierre Bertin <>
Soumis le : mercredi 19 décembre 2012 - 16:24:42
Dernière modification le : lundi 29 mai 2017 - 14:25:13
Document(s) archivé(s) le : mercredi 20 mars 2013 - 11:30:26

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PAMlowdim.pdf
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  • HAL Id : hal-00766752, version 1
  • ARXIV : 1212.4737

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INSMI | UPMC | PSL | USPC | PMA

Citation

Pierre Bertin. Very Strong Disorder for the Parabolic Anderson model in low dimensions. 2012. <hal-00766752>

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