{
  "id": "1507.01559",
  "version": "v1",
  "published": "2015-07-06T18:38:06.000Z",
  "updated": "2015-07-06T18:38:06.000Z",
  "title": "The Seneta-Heyde scaling for homogeneous fragmentations",
  "authors": [
    "Andreas E. Kyprianou",
    "Thomas Madaule"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Homogeneous mass fragmentation processes describe the evolution of a unit mass that breaks down randomly into pieces as time. Mathematically speaking, they can be thought of as continuous-time analogues of branching random walks with non-negative displacements. Following recent developments in the theory of branching random walks, in particular the work of \\cite{AShi10}, we consider the problem of the Seneta-Heyde norming of the so-called additive martingale at criticality. Aside from replicating results for branching random walks in the new setting of fragmentation processes, our main goal is to present a style of reasoning, based on $L^p$ estimates, which works for a whole host of different branching-type processes. We show that our methods apply equally to the setting of branching random walks, branching Brownian motion as well as Gaussian multiplicative chaos.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-06T18:38:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "branching random walks",
      "homogeneous fragmentations",
      "seneta-heyde scaling",
      "homogeneous mass fragmentation processes",
      "gaussian multiplicative chaos"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}