2010/10/07 by Jürgen Gärtner, Gärtner, Jürgen, Adrian Schnitzler +1
Mathematics · Physics and Astronomy · #60K37 #82C44 (Primary) 60H25 (Secondary) #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1010.1510
openalex publication_date 2010/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.