{
  "id": "math/0608740",
  "version": "v4",
  "published": "2006-08-30T13:02:33.000Z",
  "updated": "2007-12-25T03:47:14.000Z",
  "title": "Tail estimates for sums of variables sampled from a random walk",
  "authors": [
    "Roy Wagner"
  ],
  "comment": "V4: published version; theorems 1&2 slightly revised V3: Improved Bennett inequality V2: Corrected version. Confusion concerning definition of $\\beta$ resolved. Results given both in terms of sepctral gap and second largest absolute value of an eigenvalue. Sign error in statement of Theorem 4 corrected. Other minor and cosmetic corrections included as well",
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove tail estimates for variables $\\sum_i f(X_i)$, where $(X_i)_i$ is the trajectory of a random walk on an undirected graph (or, equivalently, a reversible Markov chain). The estimates are in terms of the maximum of the function $f$, its variance, and the spectrum of the graph. Our proofs are more elementary than other proofs in the literature, and our results are sharper. We obtain Bernstein and Bennett-type inequalities, as well as an inequality for subgaussian variables.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2007-12-25T03:47:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F10"
    ],
    "keywords": [
      "random walk",
      "tail estimates",
      "subgaussian variables",
      "inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......8740W"
    }
  }
}