Geometric RSK and the Toda lattice

TL;DR

This paper establishes a connection between a continuous-time geometric RSK correspondence and the Toda lattice, extending previous work that linked quantum Toda lattice with Brownian motion to a semi-classical limit.

Contribution

It introduces a new relation between continuous-time geometric RSK and the classical Toda lattice, expanding the understanding of integrable systems and combinatorial correspondences.

Findings

Established a link between continuous-time geometric RSK and Toda lattice

Extended previous quantum Toda lattice results to a semi-classical limit

Provides a new perspective on integrable systems and combinatorial mappings

Abstract

We relate a continuous-time version of the geometric RSK correspondence to the Toda lattice, in a way which can be viewed as a semi-classical limit of a recent result by the author which relates the continuous-time geometric RSK mapping, with Brownian motion as input, to the quantum Toda lattice.