# The scaling limit of the longest increasing subsequence

@inproceedings{Dauvergne2021TheSL, title={The scaling limit of the longest increasing subsequence}, author={Duncan Dauvergne and B'alint Vir'ag}, year={2021} }

We provide a framework for proving convergence to the directed landscape, the central object in the Kardar-Parisi-Zhang universality class. For last passage models, we show that compact convergence to the Airy line ensemble implies convergence to the Airy sheet. In i.i.d. environments, we show that Airy sheet convergence implies convergence of distances and geodesics to their counterparts in the directed landscape. Our results imply convergence of classical last passage models and interacting…

## 33 Citations

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