Stochastic symplectic ice

TL;DR

This paper introduces stochastic symplectic ice models with solvable structures, leading to new interacting particle systems and connections to algebraic operators, expanding the understanding of integrable stochastic models.

Contribution

It constructs novel solvable stochastic ice models with boundary conditions and links their partition functions to Demazure-Lusztig operators of type C.

Findings

Established functional equations for partition functions.

Derived recursive relations related to Demazure-Lusztig operators.

Introduced colored versions and stochastic dynamics of the models.

Abstract

In this paper, we construct solvable ice models (six-vertex models) with stochastic weights and U-turn right boundary, which we term ``stochastic symplectic ice''. The models consist of alternating rows of two types of vertices. The probabilistic interpretation of the models leads to novel interacting particle systems where particles alternately jump to the right and then to the left. Two colored versions of the models and related stochastic dynamics are also introduced. Using the Yang-Baxter equations, we establish functional equations and recursive relations for the partition functions of these models. In particular, the recursive relations satisfied by the partition function of one of the colored models are closely related to Demazure-Lusztig operators of type C.