Intermittent scaling of the probability density function tail of the Kardar-Parisi-Zhang equation

Details Intermittent scaling of the probability density function tail of the Kardar-Parisi-Zhang equation Intermittent scaling of the probability density function tail of the Kardar-Parisi-Zhang equation

2010-06-29

arxiv.org/abs/1006.5548v2

Physics

Plasma Physics

6 pages, 2 figures, submitted to EPL

Scientific paper

This letter provides the first analytical estimation of the probability density function (PDF) tail of the interface width in the Kardar-Parisi-Zhang equation in the regime of strongly non-linear growth. We find that the PDF tail is proportional to $\exp{- c w_2^{3/2}}$. In addition, the effect of spatial dimensions on the PDF tail scaling is dicussed. The PDF tail is computed by the instanton method within the Martin-Rose-Siggia framework using a careful treatment of the non-linear term. This gives a novel approach to understand the rightmost PDF tail of the interface width distribution and the analysis suggests that there is no limit in the upper critical dimension.

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