Physics – Condensed Matter – Statistical Mechanics
Scientific paper
1999-10-18
Physica A 279, 342 (2000)
Physics
Condensed Matter
Statistical Mechanics
11 pages, iopart, epsf, 2 postscript figures, submitted to Physica A, in an Addendum the distribution for the flat case is ide
Scientific paper
10.1016/S0378-4371(99)00517-8
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.
Praehofer Michael
Spohn Herbert
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