IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v166y2023ics0304414923001849.html
   My bibliography  Save this article

Large population limits of Markov processes on random networks

Author

Listed:
  • Lücke, Marvin
  • Heitzig, Jobst
  • Koltai, Péter
  • Molkenthin, Nora
  • Winkelmann, Stefanie

Abstract

We consider time-continuous Markovian discrete-state dynamics on random networks of interacting agents and study the large population limit. The dynamics are projected onto low-dimensional collective variables given by the shares of each discrete state in the system, or in certain subsystems, and general conditions for the convergence of the collective variable dynamics to a mean-field ordinary differential equation are proved. We discuss the convergence to this mean-field limit for a continuous-time noisy version of the so-called “voter model” on Erdős–Rényi random graphs, on the stochastic block model, and on random regular graphs. Moreover, a heterogeneous population of agents is studied.

Suggested Citation

  • Lücke, Marvin & Heitzig, Jobst & Koltai, Péter & Molkenthin, Nora & Winkelmann, Stefanie, 2023. "Large population limits of Markov processes on random networks," Stochastic Processes and their Applications, Elsevier, vol. 166(C).
    • Handle: RePEc:eee:spapps:v:166:y:2023:i:c:s0304414923001849
    DOI: 10.1016/j.spa.2023.09.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414923001849
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2023.09.007?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Kurtz, Thomas G., 1978. "Strong approximation theorems for density dependent Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 6(3), pages 223-240, February.
    2. F. Slanina & H. Lavicka, 2003. "Analytical results for the Sznajd model of opinion formation," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 35(2), pages 279-288, September.
    3. Sven Banischa & Ricardo Lima & Tanya Araújo, 2012. "Agent based models and opinion dynamics as markov chains," Working Papers Department of Economics 2012/10, ISEG - Lisbon School of Economics and Management, Department of Economics, Universidade de Lisboa.
    4. Keliger, Dániel & Horváth, Illés & Takács, Bálint, 2022. "Local-density dependent Markov processes on graphons with epidemiological applications," Stochastic Processes and their Applications, Elsevier, vol. 148(C), pages 324-352.
    5. Adri'an Carro & Ra'ul Toral & Maxi San Miguel, 2016. "The noisy voter model on complex networks," Papers 1602.06935, arXiv.org, revised Apr 2016.
    6. Bhamidi, Shankar & Budhiraja, Amarjit & Wu, Ruoyu, 2019. "Weakly interacting particle systems on inhomogeneous random graphs," Stochastic Processes and their Applications, Elsevier, vol. 129(6), pages 2174-2206.
    7. Jan-Hendrik Niemann & Stefan Klus & Christof Schütte, 2021. "Data-driven model reduction of agent-based systems using the Koopman generator," PLOS ONE, Public Library of Science, vol. 16(5), pages 1-23, May.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Achal Bassamboo & J. Michael Harrison & Assaf Zeevi, 2006. "Design and Control of a Large Call Center: Asymptotic Analysis of an LP-Based Method," Operations Research, INFORMS, vol. 54(3), pages 419-435, June.
    2. Luçon, Eric, 2020. "Quenched asymptotics for interacting diffusions on inhomogeneous random graphs," Stochastic Processes and their Applications, Elsevier, vol. 130(11), pages 6783-6842.
    3. Davide Crapis & Bar Ifrach & Costis Maglaras & Marco Scarsini, 2017. "Monopoly Pricing in the Presence of Social Learning," Management Science, INFORMS, vol. 63(11), pages 3586-3608, November.
    4. Ankit Gupta & Mustafa Khammash, 2022. "Frequency spectra and the color of cellular noise," Nature Communications, Nature, vol. 13(1), pages 1-18, December.
    5. Piotr Przybyła & Katarzyna Sznajd-Weron & Rafał Weron, 2014. "Diffusion Of Innovation Within An Agent-Based Model: Spinsons, Independence And Advertising," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 17(01), pages 1-22.
    6. Keliger, Dániel & Horváth, Illés, 2023. "Accuracy criterion for mean field approximations of Markov processes on hypergraphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
    7. Guzmán-Vargas, L. & Hernández-Pérez, R., 2006. "Small-world topology and memory effects on decision time in opinion dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 372(2), pages 326-332.
    8. Eminente, Clara & Artime, Oriol & De Domenico, Manlio, 2022. "Interplay between exogenous triggers and endogenous behavioral changes in contagion processes on social networks," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    9. Jamaal Ahmad & Mogens Bladt, 2022. "Phase-type representations of stochastic interest rates with applications to life insurance," Papers 2207.11292, arXiv.org, revised Nov 2022.
    10. He, Yuheng & Xue, Xiaofeng, 2023. "Moderate deviations of hitting times of a family of density-dependent Markov chains," Statistics & Probability Letters, Elsevier, vol. 195(C).
    11. Fang, Siwei & Zhao, Nan & Chen, Nan & Xiong, Fei & Yi, Yunhui, 2019. "Analyzing and predicting network public opinion evolution based on group persuasion force of populism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 809-824.
    12. Gao, Yunshi, 2024. "Large deviations for mean field model in Erdős–Rényi graph," Statistics & Probability Letters, Elsevier, vol. 205(C).
    13. Khalil, Nagi & Toral, Raúl, 2019. "The noisy voter model under the influence of contrarians," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 81-92.
    14. Ramandeep S. Randhawa & Sunil Kumar, 2009. "Multiserver Loss Systems with Subscribers," Mathematics of Operations Research, INFORMS, vol. 34(1), pages 142-179, February.
    15. Grabowski, A. & Kosiński, R.A., 2006. "Ising-based model of opinion formation in a complex network of interpersonal interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 361(2), pages 651-664.
    16. Czaplicka, Agnieszka & Charalambous, Christos & Toral, Raul & San Miguel, Maxi, 2022. "Biased-voter model: How persuasive a small group can be?," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    17. Araújo, Tanya & Fontainha, Elsa, 2017. "The specific shapes of gender imbalance in scientific authorships: A network approach," Journal of Informetrics, Elsevier, vol. 11(1), pages 88-102.
    18. Franch, Fabio & Nocciola, Luca & Vouldis, Angelos, 2024. "Temporal networks and financial contagion," Journal of Financial Stability, Elsevier, vol. 71(C).
    19. Düring, B. & Toscani, G., 2007. "Hydrodynamics from kinetic models of conservative economies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 384(2), pages 493-506.
    20. Jamol Pender & Richard Rand & Elizabeth Wesson, 2020. "A Stochastic Analysis of Queues with Customer Choice and Delayed Information," Mathematics of Operations Research, INFORMS, vol. 45(3), pages 1104-1126, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:166:y:2023:i:c:s0304414923001849. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.