## 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 the 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.

Original language | English |
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Pages (from-to) | 342-352 |

Number of pages | 11 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 279 |

Issue number | 1 |

DOIs | |

State | Published - 1 May 2000 |