Cube Root Fluctuations for the Corner Growth Model Associated to the Exclusion Process

@article{Balazs2006CubeRF,
  title={Cube Root Fluctuations for the Corner Growth Model Associated to the Exclusion Process},
  author={Marton E. Balazs and Eric A. Cator and Timo Seppalainen},
  journal={Electronic Journal of Probability},
  year={2006},
  volume={11},
  pages={1094-1132}
}
We study the last-passage growth model on the planar integer lattice with exponential weights. With boundary conditions that represent the equilibrium exclusion process as seen from a particle right after its jump we prove that the variance of the last-passage time in a characteristic direction is of order $t^{2/3}$. With more general boundary conditions that include the rarefaction fan case we show that the last-passage time fluctuations are still of order $t^{1/3}$, and also that the… 

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