KPZ equation correlations in time

@article{Corwin2019KPZEC,
  title={KPZ equation correlations in time},
  author={Ivan Corwin and Promit Ghosal and Alan Hammond},
  journal={arXiv: Probability},
  year={2019}
}
We consider the narrow wedge solution to the Kardar-Parisi-Zhang stochastic PDE under the characteristic $3:2:1$ scaling of time, space and fluctuations. We study the correlation of fluctuations at two different times. We show that when the times are close to each other, the correlation approaches one at a power-law rate with exponent $2/3$, while when the two times are remote from each other, the correlation tends to zero at a power-law rate with exponent $-1/3$. We also prove exponential-type… 

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    Proceedings of the London Mathematical Society
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In last passage percolation models lying in the KPZ universality class, long maximizing paths have a typical deviation from the linear interpolation of their endpoints governed by the two‐thirds
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