{
  "abstract": "We study comparison inequalities for contact-process-type infection dynamics on $\\mathbb Z^d$ with general local transmission mechanisms. The processes considered include both discrete-time oriented-percolation models and continuous-time contact processes in which infection events may transmit to random, possibly correlated sets of neighbouring sites. Our main results apply local-to-global comparison criteria beyond stochastic domination: if one local infection rule is more likely than another to hit every non-empty test set of neighbours, then the corresponding process has larger survival probabilities at all times. We compare classical independent-infection models with exchangeable fixed-budget, all-or-nothing, and burst-type infection mechanisms, deriving orderings for example of finite-time and infinite-time survival probabilities and stopping-time distributions. In continuous time, we further obtain consequences for critical survival thresholds of exchangeable infection laws. The results show that infection processes with identical or comparable mean-field infection intensity can nevertheless be rigorously ordered at the stochastic level once spatial geometry is taken into account. Additionally, it turns out that the classical continuous-time contact process dominates a variety of related continuous-time models, whereas its most natural discrete-time version, Bernoulli oriented percolation, is not dominant with respect to related discrete-time models.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09892",
  "author_total": 3,
  "authors": [
    {
      "name": "Benedikt Jahnel"
    },
    {
      "name": "Jonas Köppl"
    },
    {
      "name": "Pēteris Siliņš"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eq8djaav57f3m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09892",
  "fulltext_url": null,
  "id": "eq8djaav57f3m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09892",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7212121338",
  "pdf_url": "https://arxiv.org/pdf/2609.09892",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eq8djaav57f3m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2609.09892",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09892"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Comparison inequalities for discrete- and continuous-time infection processes",
  "title_text": "Comparison inequalities for discrete- and continuous-time infection processes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/eq8djaav57f3m",
  "venue": "arXiv",
  "versions": []
}