{
  "id": "2502.08568",
  "version": "v1",
  "published": "2025-02-12T16:56:51.000Z",
  "updated": "2025-02-12T16:56:51.000Z",
  "title": "Biased random walk on the critical curve of dynamical percolation",
  "authors": [
    "Assylbek Olzhabayev",
    "Dominik Schmid"
  ],
  "comment": "30 pages, 3 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study biased random walks on dynamical percolation in $\\mathbb{Z}^d$, which were recently introduced by Andres et al. We provide a second order expansion for the asymptotic speed and show for $d \\ge 2$ that the speed of the biased random walk on the critical curve is eventually monotone increasing. Our methods are based on studying the environment seen from the walker as well as a combination of ergodicity and several couplings arguments.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-02-12T16:56:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "60K37"
    ],
    "keywords": [
      "critical curve",
      "dynamical percolation",
      "study biased random walks",
      "second order expansion",
      "couplings arguments"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}