{
  "id": "2007.11998",
  "version": "v1",
  "published": "2020-07-23T13:13:05.000Z",
  "updated": "2020-07-23T13:13:05.000Z",
  "title": "Symmetric inclusion process with slow boundary: hydrodynamics and hydrostatics",
  "authors": [
    "Chiara Franceschini",
    "Patrícia Gonçalves",
    "Federico Sau"
  ],
  "comment": "35 pages, 1 figure",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study the hydrodynamic and hydrostatic limits of the one-dimensional open symmetric inclusion process with slow boundary. Depending on the value of the parameter tuning the interaction rate of the bulk of the system with the boundary, we obtain a linear heat equation with either Dirichlet, Robin or Neumann boundary conditions as hydrodynamic equation. In our approach, we combine duality and first-second class particle techniques to reduce the scaling limit of the inclusion process to the limiting behavior of a single, non-interacting, particle.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-23T13:13:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35"
    ],
    "keywords": [
      "slow boundary",
      "hydrodynamic",
      "one-dimensional open symmetric inclusion process",
      "hydrostatic",
      "first-second class particle techniques"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}