One-point distribution of the geodesic in directed last passage percolation

@article{Liu2022OnepointDO,
  title={One-point distribution of the geodesic in directed last passage percolation},
  author={Zhipeng Liu},
  journal={Probability Theory and Related Fields},
  year={2022}
}
  • Zhipeng Liu
  • Published 31 May 2021
  • Mathematics
  • Probability Theory and Related Fields
We consider the geodesic of the directed last passage percolation with iid exponential weights. We find the explicit one-point distribution of the geodesic location joint with the last passage times, and its limit as the parameters go to infinity under the KPZ scaling. 

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  • 2022
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When the geodesic becomes rigid in the directed landscape

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  • 2022
When the value L of the directed landscape at a point ( p ; q ) is sufficiently large, the geodesic from p to q is rigid and its location fluctuates of order L − 1 / 4 around its expectation. We further

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