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17 February 2025
 
  » arxiv » 1609.0264

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Local average height distribution of fluctuating interfaces
Naftali R. Smith ; Baruch Meerson ; Pavel V. Sasorov ;
Date 1 Sep 2016
AbstractHeight fluctuations of growing surfaces can be characterized by the probability distribution of height in a spatial point at a finite time. Recently, there has been spectacular progress in the studies of this quantity for the Kardar-Parisi-Zhang equation in $1+1$ dimensions. Is the finite-time one-point height distribution well defined in higher dimensions or for other surface growth models? Here we show that, at or above a critical dimension, the answer to this question is negative for a whole class of simple stochastic surface growth models. As a remedy, we introduce a emph{local average height}, whose probability density is well defined in any dimension and for all models of this class. The weak-noise theory (WNT) for these models yields the "optimal path" of the interface conditioned on a non-equilibrium fluctuation of the local average height. As an illustration, we consider the conserved Edwards-Wilkinson (EW) equation, where the finite-time one-point height distribution is ill-defined in all physical dimensions. We also determine the optimal path of the interface in a closely related problem of the finite-time emph{height-difference} distribution for the non-conserved EW equation in $1+1$ dimension.
Source arXiv, 1609.0264
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