The probability density function tail of the Kardar–Parisi–Zhang equation in the strongly non-linear regime. (23rd November 2016) - Anderson, Johan; Johansson, Jonas
Abstract: An analytical derivation of the probability density function (PDF) tail describing the strongly correlated interface growth governed by the nonlinear Kardar–Parisi–Zhang equation is provided. The PDF tail exactly coincides with a Tracy–Widom distribution i.e. a PDF tail proportional to exp ⁡ ( − c w 2 3 / 2 ), where w 2 is the the width of the interface. The PDF tail is computed by the instanton method in the strongly non-linear regime within the Martin–Siggia–Rose framework using a careful treatment of the non-linear interactions. In addition, the effect of spatial dimensions on the PDF tail scaling is discussed. This gives a novel approach to understand the rightmost PDF tail of the interface width distribution and the analysis suggests that there is no upper critical dimension.