# Stochastic higher spin vertex models on the line

### 2015/02/24

(with

Ivan Corwin)

*Comm. Math. Phys. 343 (2016), no. 2, 651-700* •

arXiv:1502.07374 [math.PR]

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.