2015/02/28 by Ivan Corwin, Leonid Petrov · 90 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Asymmetric simple exclusion process #Bethe ansatz #Markov Chains and Monte Carlo Methods #Markov process #Particle system #Probabilistic logic #Random Matrices and Applications #Simple (philosophy) #Stochastic process #Universality (dynamical systems) #Vertex (graph theory) #cond-mat.stat-mech #math-ph #math.MP #math.PR #nlin.SI
paper · pdf · doi:10.1007/s00220-015-2479-5
published in Communications in Mathematical Physics 343(2), 651-700 (Springer Science+Business Media) · 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
openalex publication_date 2015/10/17 · openalex created_date 2016/06/24 · arxiv created 2019/06/06 · arxiv updated 2019/06/07 · openalex updated_date 2026/08/05
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.