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arXiv · 1211.7125

Moments and Lyapunov exponents for the parabolic Anderson model

Alexei Borodin·Ivan Corwin
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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.

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Alexei Borodin, Ivan Corwin. 2014-04-28. Moments and Lyapunov exponents for the parabolic Anderson model. https://doi.org/10.1214/13-aap944

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