Moments and Lyapunov exponents for the parabolic Anderson model
  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. 
Alexei Borodin, Ivan Corwin
math.PR math-ph math.MP