Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2010-02-09
Nuclear Physics B 834, 523-542 (2010)
Physics
Condensed Matter
Statistical Mechanics
19 pages, 8 figures
Scientific paper
We consider the KPZ equation in one space dimension with narrow wedge initial condition, $h(x,t=0)=- |x|/\delta$, $\delta\ll 1$. 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, $t\to\infty$, 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.
Sasamoto Tomohiro
Spohn Herbert
No associations
LandOfFree
Exact height distributions for the KPZ equation with narrow wedge initial condition does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Exact height distributions for the KPZ equation with narrow wedge initial condition, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Exact height distributions for the KPZ equation with narrow wedge initial condition will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-124814