# 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} }

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.

## 2 Citations

### When the geodesic becomes rigid in the directed landscape

- MathematicsElectronic Communications in Probability
- 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…

### A conditional scaling limit of the KPZ fixed point with height tending to infinity at one location

- Mathematics
- 2022

. We consider the rare event that the height of the KPZ ﬁxed point at one ﬁxed space-time location (0 , T ) is large, and investigate the asymptotic behavior when the height tends to inﬁnity. The…

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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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