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.

References in corpus (5)

• Littelmann paths and brownian paths
• Disjoint optimizers and the directed landscape
• Minuscule reverse plane partitions via quiver representations
• Invariance of polymer partition functions under the geometric RSK correspondence
• Hidden invariance of last passage percolation and directed polymers

Cited by in corpus (4)

• The stationary horizon and semi-infinite geodesics in the directed landscape
• Positivity of the symmetric group characters is as hard as the polynomial time hierarchy
• 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