Electronic Journal of Probability
- Electron. J. Probab.
- Volume 16 (2011), paper no. 56, 1519-1548.
Time Correlations for the Parabolic Anderson Model
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.
Electron. J. Probab., Volume 16 (2011), paper no. 56, 1519-1548.
Accepted: 20 August 2011
First available in Project Euclid: 1 June 2016
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Gärtner, Jürgen; Schnitzler, Adrian. Time Correlations for the Parabolic Anderson Model. Electron. J. Probab. 16 (2011), paper no. 56, 1519--1548. doi:10.1214/EJP.v16-917. https://projecteuclid.org/euclid.ejp/1464820225