RSK in last passage percolation: a unified approach

Abstract

We present a version of the RSK correspondence based on the Pitman transform and geometric considerations. This version unifies ordinary RSK, dual RSK and continuous RSK. We show that this version is both a bijection and an isometry, two crucial properties for taking limits of last passage percolation models. We use the bijective property to give a non-computational proof that dual RSK maps Bernoulli walks to nonintersecting Bernoulli walks.

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• The stationary horizon and semi-infinite geodesics in the directed landscape
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• Estimation of the last passage percolation constant in a charged complete directed acyclic graph via perfect simulation
• Non-Markovianity of $2K-B$ and a degeneration