Stable limit laws for the parabolic Anderson model between quenched and annealed behaviour

2011/03/24 by Gärtner, Jürgen, Schnitzler, Adrian
#60F05 (Secondary) #60K37 #82C44 (Primary) 60H25 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1103.4848

Abstract

We consider the solution to the parabolic Anderson model with homogeneous initial condition in large time-dependent boxes. We derive stable limit theorems, ranging over all possible scaling parameters, for the rescaled sum over the solution depending on the growth rate of the boxes. Furthermore, we give sufficient conditions for a strong law of large numbers.

Related

• A scaling limit theorem for the parabolic Anderson model with exponential potential
• Parabolic Anderson Model in the Hyperbolic Space. Part II: Quenched Asymptotics
• Ageing in the parabolic Anderson model
• The parabolic Anderson model
• Parabolic Anderson Model in the Hyperbolic Space. Part I: Annealed Asymptotics