Moments and Lyapunov exponents for the parabolic Anderson model

Abstract

We study the parabolic Anderson model in $(1+1)$ dimensions with nearest neighbor jumps and space-time white noise (discrete space/continuous time). We prove a contour integral formula for the second moment and compute the second moment Lyapunov exponent. For the model with only jumps to the right, we prove a contour integral formula for all moments and compute moment Lyapunov exponents of all orders.

Published in at http://dx.doi.org/10.1214/13-AAP944 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (4)

• Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
• From duality to determinants for q-TASEP and ASEP
• Phase transitions for the long-time behavior of interacting diffusions
• Directed random polymers via nested contour integrals

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• Free field theory and observables of periodic Macdonald processes
• Anderson polymer in a fractional Brownian environment: asymptotic behavior of the partition function
• High moments of the SHE in the clustering regimes