{
  "abstract": "In this paper we propose lifted Markov Chains (MCs) as a new paradigm for deriving patrol strategies for mobile agents on an environment represented as a graph. Lifted MCs operate on a state space that can be larger than the set of nodes of the graph, and a projection operation maps the MC state to the corresponding node of the graph. We prove bounds on the performance improvement of lifted MCs over non-lifted MCs, where the performance is measured by the Kemeny constant, and show a corresponding monotonicity for the Stackelberg game capture probability and return-time entropy. These bounds yield a result of independent interest that relates the Kemeny constant and the MC conductance for general MCs. We also provide a tractable method for optimizing lifted MCs on general graphs with edge weights encoding travel times. Simulation results on randomly generated and real-world graphs verify that lifted MCs achieve substantial improvements, particularly on sparse graphs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10903",
  "author_total": 4,
  "authors": [
    {
      "name": "Yohan John"
    },
    {
      "name": "Gilberto Diaz-Garcia"
    },
    {
      "name": "Jason R. Marden"
    },
    {
      "name": "Francesco Bullo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/27694a61r4btf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10903",
  "fulltext_url": null,
  "id": "27694a61r4btf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10903",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.SY"
    ],
    [
      "arxiv",
      "eess.SY"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1705|Optimization and Search Problems"
    ]
  ],
  "openalex": "W7221168677",
  "pdf_url": "https://arxiv.org/pdf/2610.10903",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/27694a61r4btf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.10903",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10903"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Deceptive Stochastic Patrolling via Markov Chain Lifting",
  "title_text": "Deceptive Stochastic Patrolling via Markov Chain Lifting",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/27694a61r4btf",
  "venue": "arXiv",
  "versions": []
}