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Stochasticization of Solutions to the Yang-Baxter Equation

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arxiv 1810.04299 v1 pith:D7R2CUHX submitted 2018-10-09 math.PR math-phmath.MP

Amol Aggarwal , Alexei Borodin , Alexey Bufetov This is my paper · ORCID
classification math.PRmath-phmath.MP
keywords equationyang-baxtersolutionstochasticdynamicalproceduresolutionsstochasticization
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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.

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