Geometric RSK and the Toda lattice

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.

v2: minor corrections

References in corpus (3)

• Geometric RSK correspondence, Whittaker functions and symmetrized random polymers
• Littelmann paths and brownian paths
• A q-weighted version of the Robinson-Schensted algorithm

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• Stochastic Bäcklund transformations
• Interlacing networks: birational RSK, the octahedron recurrence, and Schur function identities
• The Poisson Geometry of Plancherel Formulas for Triangular Groups
• Matrix Orthogonal Polynomials, non-abelian Toda lattice and Bäcklund transformation
• A Path-Counting Analysis of Phase Shifts in Box-Ball Systems
• Discrete Whittaker processes