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.
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https://hal.archives-ouvertes.fr/hal-00766752
Contributor : Pierre Bertin <>
Submitted on : Wednesday, December 19, 2012 - 4:24:42 PM
Last modification on : Tuesday, May 14, 2019 - 10:59:47 AM
Long-term archiving on: Wednesday, March 20, 2013 - 11:30:26 AM

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

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

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