{
  "id": "1605.08414",
  "version": "v1",
  "published": "2016-05-26T19:23:24.000Z",
  "updated": "2016-05-26T19:23:24.000Z",
  "title": "The frog model with drift on R",
  "authors": [
    "Josh Rosenberg"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Consider a Poisson process on $\\mathbb R$ with intensity $f$ where $0 \\leq f(x)<\\infty$ for ${x}\\geq 0$ and ${f(x)}=0$ for $x<0$. The \"points\" of the process represent sleeping frogs. In addition, there is one active frog initially located at the origin. At time ${t}=0$ this frog begins performing Brownian motion with leftward drift $\\lambda$ (i.e. its motion is a random process of the form ${B}_{t}-\\lambda {t}$). Any time an active frog arrives at a point where a sleeping frog is residing, the sleeping frog becomes active and begins performing Brownian motion with leftward drift $\\lambda$, independently of the motion of all of the other active frogs. This paper establishes sharp conditions on the intensity function $f$ that determine whether the model is transient (meaning the probability that infinitely many frogs return to the origin is 0), or non-transient (meaning this probability is greater than 0).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-26T19:23:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "frog model",
      "active frog",
      "paper establishes sharp conditions",
      "frog begins performing brownian motion",
      "leftward drift"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}