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arXiv · 1810.04299

Stochasticization of Solutions to the Yang-Baxter Equation

Amol Aggarwal·Alexei Borodin·Alexey Bufetov
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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.

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Amol Aggarwal, Alexei Borodin, Alexey Bufetov. 2018-10-09. Stochasticization of Solutions to the Yang-Baxter Equation. https://doi.org/10.1007/s00023-019-00799-y

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