Stochastic higher spin vertex models on the line

Abstract

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, ASEP, the stochastic six-vertex model, q-TASEP 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.

40 pages, 10 figures. v2: Removed incorrect duality statement and usages of incorrect Plancherel theory for finite vertical spins. Erratum to be submitted to the journal

References in corpus (1)

• Log-Gamma directed polymer with fixed endpoints via the replica Bethe Ansatz

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• Observables of coloured stochastic vertex models and their polymer limits
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• Random walk on nonnegative integers in beta distributed random environment
• Limiting current distribution for a two species asymmetric exclusion process
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• Markov duality and Bethe ansatz formula for half-line open ASEP
• Hidden diagonal integrability of $q$-Hahn vertex model and Beta polymer model
• KPZ fluctuations in finite volume
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• Log-gamma directed polymer with one free end via coordinate Bethe Ansatz
• Tracy-Widom asymptotics for a river delta model
• The stochastic telegraph equation limit of the stochastic higher spin six vertex model
• Stochastic PDE limit of the dynamic ASEP
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