From the Lifshitz tail to the quenched survival asymptotics in the trapping problem.

Fukushima, Ryoki

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Potential confinement property of the parabolic Anderson model

Gabriela Grüninger, Wolfgang König (2009)

Annales de l'I.H.P. Probabilités et statistiques

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We consider the parabolic Anderson model, the Cauchy problem for the heat equation with random potential in ℤ. We use i.i.d. potentials :ℤ→ℝ in the third universality class, namely the class of , in the classification of van der Hofstad, König and Mörters [ (2006) 307–353]. This class consists of potentials whose logarithmic moment generating function is regularly varying with parameter =1, but do not belong to the class of so-called double-exponentially distributed potentials...