Scale Invariance of the PNG Droplet and the Airy Process

@article{Praehofer2001ScaleIO,
  title={Scale Invariance of the PNG Droplet and the Airy Process},
  author={Michael Praehofer and Herbert Spohn},
  journal={Journal of Statistical Physics},
  year={2001},
  volume={108},
  pages={1071-1106}
}
We establish that the static height fluctuations of a particular growth model, the PNG droplet, converges upon proper rescaling to a limit process, which we call the Airy process A(y). The Airy process is stationary, it has continuous sample paths, its single “time” (fixed y) distribution is the Tracy–Widom distribution of the largest eigenvalue of a GUE random matrix, and the Airy process has a slow decay of correlations as y−2. Roughly the Airy process describes the last line of Dyson's… 
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