RSK in last passage percolation: a unified approach

TL;DR

This paper introduces a unified RSK correspondence based on the Pitman transform, unifying various RSK variants and establishing key properties for analyzing last passage percolation models.

Contribution

It presents a new RSK framework that unifies ordinary, dual, and continuous RSK using geometric methods, proving bijectivity and isometry.

Findings

Unified RSK version is a bijection and an isometry

Provides a non-computational proof for dual RSK mapping Bernoulli walks

Facilitates limit analysis of last passage percolation models

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.