{
  "id": "1908.02359",
  "version": "v1",
  "published": "2019-08-06T20:40:12.000Z",
  "updated": "2019-08-06T20:40:12.000Z",
  "title": "Stochastic Fusion of Interacting Particle Systems and Duality Functions",
  "authors": [
    "Jeffrey Kuan"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We introduce a new method, which we call stochastic fusion, which takes an exclusion process and constructs an interacting particle systems in which more than one particle may occupy a lattice site. The construction only requires the existence of stationary measures of the original exclusion process on a finite lattice. If the original exclusion process satisfies Markov duality on a finite lattice, then the construction produces Markov duality functions (for some initial conditions) for the fused exclusion process. The stochastic fusion construction is based off of the Rogers--Pitman intertwining. In particular, we have results for three types of models: 1. For symmetric exclusion processes, the fused process and duality functions are inhomogeneous generalizations of those in \\cite{GKRV}. The construction also allows a general class of open boundary conditions: as an application of the duality, we find the hydrodynamic limit and stationary measures of the generalized symmetric simple exclusion process SSEP$(m/2)$ on $\\mathbb{Z}_+$ for open boundary conditions. 2. For the asymmetric simple exclusion process, the fused process and duality functions are inhomogeneous generalizations of those found in \\cite{CGRS} for the ASEP$(q,j)$. As a by-product of the construction, we show that the multi--species ASEP$(q,j)$ preserves $q$--exchangeable measures, and use this to find new duality functions for the ASEP, ASEP$(q,j)$ and $q$--Boson. 3. For dynamic models, we fuse the dynamic ASEP from \\cite{BorodinDyn}, and produce a dynamic and inhomogeneous version of ASEP$(q,j)$. We also apply stochastic fusion to IRF models and compare them to previously found models.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-06T20:40:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "interacting particle systems",
      "stochastic fusion",
      "symmetric simple exclusion process",
      "produces markov duality functions",
      "process satisfies markov duality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}