Non symmetric Cauchy kernel, crystals and last passage percolation

TL;DR

This paper connects non-symmetric Cauchy kernels with last passage percolation models using Demazure characters, employing crystal basis theory and RSK correspondence restrictions to derive new probabilistic laws.

Contribution

It introduces a novel approach linking non-symmetric Cauchy kernels, Demazure characters, and crystal basis theory to analyze last passage percolation models.

Findings

Derived explicit laws for last passage percolation models

Unified RSK restriction framework compatible with crystal basis theory

Established connections between algebraic identities and probabilistic models

Abstract

We use non-symmetric Cauchy kernel identities to get the law of last passagepercolation models in terms of Demazure characters. The construction is basedon some restrictions of the RSK correspondence that we rephrase in a unifiedway which is compatible with crystal basis theory.