Statistical Self-Similarity of One-Dimensional Growth Processes

  title={Statistical Self-Similarity of One-Dimensional Growth Processes},
  author={Michael Pr{\"a}hofer and Herbert Spohn},
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… CONTINUE READING