Functional laws of the iterated logarithm for local times of recurrent random walks on
Endre Csáki, Pál Révész, Jay Rosen (1998)
Annales de l'I.H.P. Probabilités et statistiques
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The parabolic Anderson model is the Cauchy problem for the heat equation with a random potential. We consider this model in a setting which is continuous in time and discrete in space, and focus on time-constant, independent and identically distributed potentials with polynomial tails at infinity. We are concerned with the long-term temporal dynamics of this system. Our main result is that the periods, in which the profile of the solutions remains nearly constant, are increasing linearly...