{
  "id": "2412.19752",
  "version": "v1",
  "published": "2024-12-27T17:21:41.000Z",
  "updated": "2024-12-27T17:21:41.000Z",
  "title": "A random walk among random graphs",
  "authors": [
    "Nicolas Curien"
  ],
  "comment": "are very welcome! Do not hesitate",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "Lecture notes of a master course given at Orsay between 2019-2024. Topics covered include Part I: One-dimensional random walks, cycle lemma and Bienaym\\'e--Galton--Watson random trees. Part II: Erd\\\"os--R\\'enyi random graphs, three proofs of the emergence of the giant component. Part III: Random recursive tree, random permutations and continuous time embedding techniques. Intended for publication.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-12-27T17:21:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random graphs",
      "one-dimensional random walks",
      "bienayme-galton-watson random trees",
      "master course",
      "cycle lemma"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}