{
  "id": "cond-mat/0603243",
  "version": "v1",
  "published": "2006-03-09T12:02:58.000Z",
  "updated": "2006-03-09T12:02:58.000Z",
  "title": "Stochastic Deformations of Sample Paths of Random Walks and Exclusion Models",
  "authors": [
    "Guy Fayolle",
    "Cyril Furtlehner"
  ],
  "comment": "Conference Proceedings, MathInfo2004, Vienna, 15 pages, 1 figure",
  "journal": "In Mathematics and computer science. III, Trends Math., pages 415--428. Birkh\\\"auser, Basel, 2004",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.other"
  ],
  "abstract": "This study in centered on models accounting for stochastic deformations of sample paths of random walks, embedded either in $\\mathbb{Z}^2$ or in $\\mathbb{Z}^3$. These models are immersed in multi-type particle systems with exclusion. Starting from examples, we give necessary and sufficient conditions for the underlying Markov processes to be reversible, in which case their invariant measure has a Gibbs form. Letting the size of the sample path increase, we find the convenient scalings bringing to light phase transition phenomena. Stable and metastable configurations are bound to time-periods of limiting deterministic trajectories which are solution of nonlinear differential systems: in the example of the ABC model, a system of Lotka-Volterra class is obtained, and the periods involve elliptic, hyper-elliptic or more general functions. Lastly, we discuss briefly the contour of a general approach allowing to tackle the transient regime via differential equations of Burgers' type.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-03-09T12:02:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random walks",
      "stochastic deformations",
      "exclusion models",
      "light phase transition phenomena",
      "sample path increase"
    ],
    "tags": [
      "conference paper",
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006cond.mat..3243F"
    }
  }
}