The probability density function tail of the Kardar-Parisi-Zhang equation in the strongly non-linear regime
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 (cw2 3/2), Where w 2 is the the width of the interface. The PDF tail is computed by the instanton method in t