{
  "abstract": "Stochastic search processes in which agents are continuously inserted into and removed from a target search domain are fundamental to a wide class of physical and artificial systems. The theory of such non-conservative search processes is, however, much less developed than for search processes with a fixed number of agents. Recent work on the non-conservative case has characterized the fastest first-passage time (FPT) to a target, after which the search process is terminated. Here we consider the complementary problem of continuous arrival statistics to a target. In particular, we derive the full time-dependent distribution of target arrivals, which we use to show that the inter-arrival time distribution is exactly exponential in steady-state regardless of the underlying search process. Thus, counterintuitively, the arrival statistics of non-conservative search are both universal and much simpler than sequential search-and-capture processes involving a fixed number of agents. Our methods also yield an exact expression for the fastest FPT distribution with time-dependent insertion, thereby generalizing previous work on fixed-rate insertion for non-conservative search. Altogether these results have major implications for target resource accumulation, wherein the delivery of resources is counter-balanced by their downstream consumption.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.16025",
  "author_total": 3,
  "authors": [
    {
      "name": "José Giral-Barajas"
    },
    {
      "name": "Samantha Linn"
    },
    {
      "name": "Paul C. Bressloff"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3rwb06a3ne8hy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.16025",
  "fulltext_url": null,
  "id": "3rwb06a3ne8hy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.16025",
  "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",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "1312|Diffusion and Search Dynamics"
    ]
  ],
  "openalex": "W7164939982",
  "pdf_url": "https://arxiv.org/pdf/2606.16025",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3rwb06a3ne8hy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:36Z",
      "native_id": "2606.16025",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.16025"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Universality in the target arrival statistics of non-conservative search processes",
  "title_text": "Universality in the target arrival statistics of non-conservative search processes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/3rwb06a3ne8hy",
  "venue": "arXiv",
  "versions": []
}