{
  "abstract": "We introduce a general class of interacting reinforced stochastic systems evolving on a network. The dynamics are governed by two distinct interaction structures: a sampling network, which determines how information is acquired, and a reinforcement network, which determines how the sampled information influences future evolution. Processes generate Bernoulli observations through preferential, de-preferential, or mixed sampling, while observations are transmitted through an edge-dependent affine reinforcement mechanism. We formulate the dynamics as a stochastic approximation scheme and study their asymptotic behaviour. We establish sufficient conditions for almost sure convergence to a deterministic limit and, when the sampling and reinforcement graphs coincide, derive graph-theoretic criteria involving odd cycles, mixed-sampling vertices, and subcritical reinforcement. Under additional structural assumptions, we establish almost sure convergence and partial synchronization in a random-limit regime. In the deterministic regime, we also prove a law of the iterated logarithm and a central limit theorem under suitable spectral and regularity conditions. Finally, we show how the framework encompasses interacting urn models with edge-dependent reinforcement, urns with memory, and random walks with memory.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13884",
  "author_total": 3,
  "authors": [
    {
      "name": "Yogesh Dahiya"
    },
    {
      "name": "Gursharn Kaur"
    },
    {
      "name": "Neeraja Sahasrabudhe"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d1vcgm94s7t4t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13884",
  "fulltext_url": null,
  "id": "d1vcgm94s7t4t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13884",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7221532685",
  "pdf_url": "https://arxiv.org/pdf/2610.13884",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d1vcgm94s7t4t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.13884",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13884"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Interacting Stochastic Systems with Agent-Based Sampling and Connection-Based Reinforcement",
  "title_text": "Interacting Stochastic Systems with Agent-Based Sampling and Connection-Based Reinforcement",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/d1vcgm94s7t4t",
  "venue": "arXiv",
  "versions": []
}