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Exact Short-Time Height Distribution in the One-Dimensional Kardar-Parisi-Zhang Equation and Edge Fermions at High Temperature
Physical Review Letters
We consider the early time regime of the Kardar-Parisi-Zhang (KPZ) equation in 1+1 dimensions in curved (or droplet) geometry. We show that for short time t, the probability distribution P(H,t) of the height H at a given point x takes the scaling form P(H,t) ∼(-Φ_ drop(H)/√(t)) where the rate function Φ_ drop(H) is computed exactly. While it is Gaussian in the center, i.e., for small H, the PDF has highly asymmetric non-Gaussian tails which we characterize in detail. This function Φ_ drop(H) isdoi:10.1103/physrevlett.117.070403 pmid:27563940 fatcat:ixt3eszfoncyppbhl7vw5h5xxy