{
  "id": "cond-mat/9812205",
  "version": "v1",
  "published": "1998-12-11T19:12:11.000Z",
  "updated": "1998-12-11T19:12:11.000Z",
  "title": "Statistics of knots and entangled random walks",
  "authors": [
    "Sergei Nechaev"
  ],
  "comment": "Extended version of lectures presented at Les Houches 1998 summer school \"Topological Aspects of Low Dimensional Systems\", July 7 - 31, 1998; revtex, 79 pages, 16 eps-figures",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.soft",
    "math.PR"
  ],
  "abstract": "The lectures review the state of affairs in modern branch of mathematical physics called probabilistic topology. In particular we consider the following problems: (i) We estimate the probability of a trivial knot formation on the lattice using the Kauffman algebraic invariants and show the connection of this problem with the thermodynamic properties of 2D disordered Potts model; (ii) We investigate the limit behavior of random walks in multi-connected spaces and on non-commutative groups related to the knot theory. We discuss the application of the above mentioned problems in statistical physics of polymer chains. On the basis of non-commutative probability theory we derive some new results in statistical physics of entangled polymer chains which unite rigorous mathematical facts with more intuitive physical arguments.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-12-11T19:12:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "entangled random walks",
      "statistics",
      "polymer chains",
      "statistical physics",
      "2d disordered potts model"
    ],
    "tags": [
      "lecture notes"
    ],
    "note": {
      "typesetting": "RevTeX",
      "pages": 79,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 485447,
      "adsabs": "1999tald.conf..643N"
    }
  }
}