{
  "id": "math/0009040",
  "version": "v1",
  "published": "2000-09-04T22:44:57.000Z",
  "updated": "2000-09-04T22:44:57.000Z",
  "title": "Second class particles as microscopic characteristics in totally asymmetric nearest-neighbor K-exclusion processes",
  "authors": [
    "Timo Seppalainen"
  ],
  "comment": "32 pages",
  "journal": "Trans. Amer. Math. Soc. 353 (2001) 4801-4829",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study aspects of the hydrodynamics of one-dimensional totally asymmetric K-exclusion, building on the hydrodynamic limit of Seppalainen (1999). We prove that the weak solution chosen by the particle system is the unique one with maximal current past any fixed location. A uniqueness result is needed because we can prove neither differentiability nor strict concavity of the flux function, so we cannot use the Lax-Oleinik formula or jump conditions to define entropy solutions. Next we prove laws of large numbers for a second class particle in K-exclusion. The macroscopic trajectories of second class particles are characteristics and shocks of the conservation law for the particle density. In particular, we extend to K-exclusion Ferrari's result that the second class particle follows a macroscopic shock in the Riemann solution. The technical novelty of the proofs is a variational representation for the position of a second class particle, in the context of the variational coupling method.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-09-04T22:44:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82C22"
    ],
    "keywords": [
      "second class particle",
      "totally asymmetric nearest-neighbor k-exclusion processes",
      "microscopic characteristics",
      "weak solution chosen"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Trans. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math......9040S"
    }
  }
}