Short-time height distribution in 1d KPZ equation: starting from a parabola

  title={Short-time height distribution in 1d KPZ equation: starting from a parabola},
  author={Alex Kamenev and Baruch Meerson and Pavel Sasorov},
We study the probability distribution P(H, t, L) of the surface height h(x = 0, t) = H in the Kardar-Parisi-Zhang (KPZ) equation in 1 + 1 dimension when starting from a parabolic interface, h(x, t = 0) = x/L. The limits of L → ∞ and L → 0 have been recently solved exactly for any t > 0. Here we address the early-time behavior of P(H, t, L) for general L. We employ the weak-noise theory a variant of WKB approximation – which yields the optimal history of the interface, conditioned on reaching… 

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Changing the sign of λ is equivalent to changing the sign of h