Stochastic Higher Spin Vertex Models on the Line


We introduce a four-parameter family of interacting particle systems on the line, which can be diagonalized explicitly via a complete set of Bethe ansatz eigenfunctions, and which enjoy certain Markov dualities. Using this, for the systems started in step initial data, we write down nested contour integral formulas for moments and Fredholm determinant formulas for Laplace-type transforms. Taking various choices or limits of parameters, this family degenerates to many of the known exactly solvable models in the Kardar–Parisi–Zhang universality class, as well as leads to many new examples of such models. In particular, asymmetric simple exclusion process, the stochastic six-vertex model, q-totally asymmetric simple exclusion process and various directed polymer models all arise in this manner. Our systems are constructed from stochastic versions of the R-matrix related to the six-vertex model. One of the key tools used here is the fusion of R-matrices and we provide a probabilistic proof of this procedure.

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  • 06 August 2019

    This is an erratum to the paper [CP16]. The aim of this note is to address two separate errors in the paper.

  • 06 August 2019

    This is an erratum to the paper [CP16]. The aim of this note is to address two separate errors in the paper.


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Correspondence to Ivan Corwin.

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Communicated by N. Reshetikhin

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Corwin, I., Petrov, L. Stochastic Higher Spin Vertex Models on the Line. Commun. Math. Phys. 343, 651–700 (2016).

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  • High Spin
  • Exclusion Process
  • Corwin
  • Totally Asymmetric Simple Exclusion Process
  • Vertex Weight