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

Jürgen Gärtner; Adrian Schnitzler

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arXiv · 1103.4848

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

Jürgen Gärtner·Adrian Schnitzler

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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.

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Jürgen Gärtner, Adrian Schnitzler. 2012-11-04. Stable limit laws for the parabolic Anderson model between quenched and annealed behaviour. https://arxiv.org/abs/1103.4848

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