Stochasticization of Solutions to the Yang-Baxter Equation

TL;DR

This paper introduces a novel stochasticization procedure that transforms existing solutions to the Yang-Baxter equation into stochastic solutions, leading to new solutions for elliptic, higher rank, and tetrahedron equations.

Contribution

The paper presents a new method to generate stochastic solutions from known Yang-Baxter solutions, expanding the set of available solutions for various forms of the equation.

Findings

Developed a stochasticization procedure for Yang-Baxter solutions

Produced new stochastic elliptic and higher rank solutions

Derived a stochastic solution to a dynamical tetrahedron equation

Abstract

In this paper we introduce a procedure that, given a solution to the Yang-Baxter equation as input, produces a stochastic (or Markovian) solution to (a possibly dynamical version of) the Yang-Baxter equation. We then apply this "stochasticization procedure" to obtain three new, stochastic solutions to several different forms of the Yang-Baxter equation. The first is a stochastic, elliptic solution to the dynamical Yang-Baxter equation; the second is a stochastic, higher rank solution to the dynamical Yang-Baxter equation; and the third is a stochastic solution to a dynamical variant of the tetrahedron equation.