Statistical Self-Similarity of One-Dimensional Growth Processes

Abstract

For one-dimensional growth processes we consider the distribution of the height above a given point of the substrate and study its scale invariance in the limit of large times. We argue that for self-similar growth from a single seed the universal distribution is the Tracy-Widom distribution from the theory of random matrices and that for growth from a flat substrate it is some other, only numerically determined distribution. In particular, for the polynuclear growth model in the droplet geometry the height maps onto the longest increasing subsequence of a random permutation, from which the height distribution is identified as the Tracy-Widom distribution.

11 pages, iopart, epsf, 2 postscript figures, submitted to Physica A, in an Addendum the distribution for the flat case is identified analytically

References in corpus (1)

• Scale Invariant Dynamics of Surface Growth

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