{
  "id": "1510.04870",
  "version": "v1",
  "published": "2015-10-16T13:10:18.000Z",
  "updated": "2015-10-16T13:10:18.000Z",
  "title": "How to initialize a second class particle?",
  "authors": [
    "Márton Balázs",
    "Attila László Nagy"
  ],
  "comment": "25 pages, 3 figures",
  "categories": [
    "math.PR",
    "cond-mat.stat-mech"
  ],
  "abstract": "We greatly generalize P. A. Ferrari and C. Kipnis' results on the behavior of the second class particle in the rarefaction fan of the totally asymmetric simple exclusion process (Ann. Inst. H. Poincar\\'e Probab. Statist., 31(1), 1995). Versions of their results are shown to hold through for practically any attractive particle system (including zero-range, misanthrope models, and many more) with established hydrodynamic behavior. The main novelty is a careful choice of the particular initial distribution at the site of the second class particle that makes the extension possible. Combined with strong recent results in hydrodynamic limits, we are able to identify the ballistically and diffusively rescaled limit distribution of the second class particle position in a wide range of asymmetric and symmetric models, respectively. We also point out a model with non-concave, non-convex hydrodynamics, where the rescaled second class particle distribution has both continuous and discrete counterparts. As a by-product of our methods we reveal a very interesting invariance property of the one-site marginal distribution of the process underneath the second class particle. Finally, we give a lower estimate on the probability of survival of a second class particle-antiparticle pair.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-16T13:10:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82C22"
    ],
    "keywords": [
      "rescaled second class particle distribution",
      "second class particle position",
      "totally asymmetric simple exclusion process",
      "second class particle-antiparticle pair",
      "one-site marginal distribution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151004870B"
    }
  }
}