Alexei Borodin, Ivan Corwin
Published 2012-11-30, updated 2014-04-28Version 3
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.
Comments: 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)
Journal: Annals of Applied Probability 2014, Vol. 24, No. 3, 1172-1198
The universality classes in the parabolic Anderson model
Localisation and ageing in the parabolic Anderson model with Weibull potential
The third moment for the parabolic Anderson model
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