{
  "id": "0901.1790",
  "version": "v2",
  "published": "2009-01-13T14:19:03.000Z",
  "updated": "2009-03-05T14:47:51.000Z",
  "title": "Note on the Transition to Intermittency for the exponential of the Square of a Steinhaus Series",
  "authors": [
    "Philippe Mounaix",
    "Pierre Collet"
  ],
  "comment": "REVTeX file, 12 pages, changed introduction and added references, accepted by J. Phys. A",
  "journal": "J. Phys. A: Math. Theor. 42 (2009) 165207",
  "doi": "10.1088/1751-8113/42/16/165207",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "Intermittency of $\\mathcal{E}_N(x,g)=\\exp\\lbrack g| S_N(x)|^2\\rbrack$ as $N\\to +\\infty$ is investigated on a $d$-dimensional torus $\\Lambda$, when $S_N(x)$ is a finite Steinhaus series of $(2N+1)^d$ terms normalized to $<| S_N(x)|^2> =1$. Assuming ergodicity of $\\mathcal{E}_N(x,g)$ as $N\\to +\\infty$ in the domain $g<1$, where $\\lim_{N\\to +\\infty}<\\mathcal{E}_N(g)>$ exists, transition to intermittency is proved as $g$ increases past the threshold $g_{th}=1$. This transition goes together with a transition from (assumed) ergodicity at $g<g_{th}$ to a regime where $\\lim_{N\\to +\\infty}\\lbrack|\\Lambda|<\\mathcal{E}_N(g)>\\rbrack^{-1}\\int_{\\Lambda}\\mathcal{E}_N(x,g) d^dx=0$ at $g>g_{th}$. In this asymptotic sense one can say that ergodicity is lost as $g$ increases past the value $g=1$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-03-05T14:47:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G60",
      "82D10"
    ],
    "keywords": [
      "transition",
      "intermittency",
      "exponential",
      "increases past",
      "finite steinhaus series"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics A Mathematical General",
      "year": 2009,
      "month": "Apr",
      "volume": 42,
      "number": 16,
      "pages": 165207
    },
    "note": {
      "typesetting": "RevTeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009JPhA...42p5207M"
    }
  }
}