{
  "id": "1403.5903",
  "version": "v2",
  "published": "2014-03-24T10:39:56.000Z",
  "updated": "2017-07-03T13:19:58.000Z",
  "title": "Systems of interacting diffusions with partial annihilation through membranes",
  "authors": [
    "Zhen-Qing Chen",
    "Wai-Tong Fan"
  ],
  "comment": "Published at http://dx.doi.org/10.1214/15-AOP1047 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2017, Vol. 45, No. 1, 100-146",
  "doi": "10.1214/15-AOP1047",
  "categories": [
    "math.PR"
  ],
  "abstract": "We introduce an interacting particle system in which two families of reflected diffusions interact in a singular manner near a deterministic interface $I$. This system can be used to model the transport of positive and negative charges in a solar cell or the population dynamics of two segregated species under competition. A related interacting random walk model with discrete state spaces has recently been introduced and studied in Chen and Fan (2014). In this paper, we establish the functional law of large numbers for this new system, thereby extending the hydrodynamic limit in Chen and Fan (2014) to reflected diffusions in domains with mixed-type boundary conditions, which include absorption (harvest of electric charges). We employ a new and direct approach that avoids going through the delicate BBGKY hierarchy.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-03-24T10:39:56.000Z",
      "title": "Systems of interacting diffusions with annihilation through membranes",
      "abstract": "We introduce an interacting particle system in which two families of reflected diffusions interact in a singular manner near a deterministic interface $I$. This system can be used to model the transport of positive and negative charges in a solar cell or the population dynamics of two segregated species under competition. A related interacting random walk model with discrete state spaces has recently been introduced and studied in [9]. In this paper, we establish the functional law of large numbers for this new system, thereby extending the hydrodynamic limit in [9] to reflected diffusions in domains with mixed-type boundary conditions, which include absorption (harvest of electric charges). We employ a new and direct approach that avoids going through the delicate BBGKY hierarchy.",
      "comment": "37 pages, 1 figure",
      "journal": null,
      "doi": null,
      "authors": [
        "Zhen-Qing Chen",
        "Wai-Tong",
        "Fan"
      ]
    },
    {
      "version": "v2",
      "updated": "2017-07-03T13:19:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "interacting diffusions",
      "annihilation",
      "related interacting random walk model",
      "discrete state spaces",
      "mixed-type boundary conditions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.5903C"
    }
  }
}