The third moment for the parabolic Anderson model

الأصل · EN

In this paper, we study the parabolic Anderson model starting from the Dirac delta initial data: (∂/∂ t -ν2∂²/∂ x²) u(t,x) = λu(t,x) W(t,x), u(0,x)=δ₀(x), x, where W denotes the space-time white noise. By evaluating the threefold contour integral in the third moment formula by Borodin and Corwin [2], we obtain some explicit formulas for E[u(t,x)³]. One application of these formulas is given to show the exact phase transition for the intermittency front of order three.