{
  "id": "math/0309359",
  "version": "v1",
  "published": "2003-09-22T10:59:35.000Z",
  "updated": "2003-09-22T10:59:35.000Z",
  "title": "Local Limit Theorem for the Lorentz Process and Its Recurrence in the Plane",
  "authors": [
    "Domokos Szász",
    "Tamás Varjú"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "For Young systems, i.e. for hyperbolic systems without/with singularities satisfying Lai-Sang Young's axioms (which imply exponential decay of correlation and the CLT) a local CLT is proven. In fact, a unified version of the local CLT is found, covering among others the absolutely contionuous and the arithmetic cases. For the planar Lorentz process with a finite horizon this result implies a.) the local CLT and b.) the recurrence. For the latter case ($d=2$, finite horizon), combining the global CLT with abstract ergodic theoretic ideas, K. Schmidt, and J.-P. Conze, could already establish recurrence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-09-22T10:59:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D50",
      "60F05",
      "37A50",
      "37A60"
    ],
    "keywords": [
      "local limit theorem",
      "lorentz process",
      "singularities satisfying lai-sang youngs",
      "satisfying lai-sang youngs axioms",
      "without/with singularities satisfying lai-sang"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......9359S"
    }
  }
}