Exact height distributions for the KPZ equation with narrow wedge initial condition

DOI10.1016/J.NUCLPHYSB.2010.03.026zbMATH Open1204.35137arXiv1002.1879OpenAlexW2144330969MaRDI QIDQ622743

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Publication date: 3 February 2011

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Abstract: We consider the KPZ equation in one space dimension with narrow wedge initial condition, $h(x,t=0)=-|x|/delta$, $deltall1$. Based on previous results for the weakly asymmetric simple exclusion process with step initial conditions, we obtain a determinantal formula for the one-point distribution of the solution $h(x,t)$ valid for any $x$ and $t>0$. The corresponding distribution function converges in the long time limit, $toinfty$, to the Tracy-Widom distribution. The first order correction is a shift of order $t^{-1/3}$. We provide numerical computations based on the exact formula.

Full work available at URL: https://arxiv.org/abs/1002.1879

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