Stochasticization of Solutions to the Yang–Baxter 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.