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2011 Time Correlations for the Parabolic Anderson Model
Jürgen Gärtner, Adrian Schnitzler
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Electron. J. Probab. 16: 1519-1548 (2011). DOI: 10.1214/EJP.v16-917

Abstract

We derive exact asymptotics of time correlation functions for the parabolic Anderson model with homogeneous initial condition and time-independent tails that decay more slowly than those of a double exponential distribution and have a finite cumulant generating function. We use these results to give precise asymptotics for statistical moments of positive order. Furthermore, we show what the potential peaks that contribute to the intermittency picture look like and how they are distributed in space. We also investigate for how long intermittency peaks remain relevant in terms of ageing properties of the model.

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Jürgen Gärtner. Adrian Schnitzler. "Time Correlations for the Parabolic Anderson Model." Electron. J. Probab. 16 1519 - 1548, 2011. https://doi.org/10.1214/EJP.v16-917

Information

Accepted: 20 August 2011; Published: 2011
First available in Project Euclid: 1 June 2016

zbMATH: 1245.60100
MathSciNet: MR2827469
Digital Object Identifier: 10.1214/EJP.v16-917

Subjects:
Primary: 60K37, 82C44
Secondary: 60H25

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Vol.16 • 2011
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