{
  "id": "cond-mat/0604159",
  "version": "v1",
  "published": "2006-04-06T07:59:43.000Z",
  "updated": "2006-04-06T07:59:43.000Z",
  "title": "Multiple phases in stochastic dynamics: geometry and probabilities",
  "authors": [
    "B. Gaveau",
    "L. S. Schulman"
  ],
  "journal": "Phys. Rev. E 73, 036124 (2006)",
  "doi": "10.1103/PhysRevE.73.036124",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.other"
  ],
  "abstract": "Stochastic dynamics is generated by a matrix of transition probabilities. Certain eigenvectors of this matrix provide observables, and when these are plotted in the appropriate multi-dimensional space the phases (in the sense of phase transitions) of the underlying system become manifest as extremal points. This geometrical construction, which we call an \\textit{observable-representation of state space}, can allow hierarchical structure to be observed. It also provides a method for the calculation of the probability that an initial points ends in one or another asymptotic state.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-04-06T07:59:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stochastic dynamics",
      "multiple phases",
      "probability",
      "initial points ends",
      "appropriate multi-dimensional space"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. E"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}