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Graphon particle system: Uniform-in-time concentration bounds

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  • Bayraktar, Erhan
  • Wu, Ruoyu

Abstract

In this paper, we consider graphon particle systems with heterogeneous mean-field type interactions and the associated finite particle approximations. Under suitable growth (resp. convexity) assumptions, we obtain uniform-in-time concentration estimates, over finite (resp. infinite) time horizon, for the Wasserstein distance between the empirical measure and its limit, extending the work of Bolley–Guillin–Villani (2007).

Suggested Citation

  • Bayraktar, Erhan & Wu, Ruoyu, 2023. "Graphon particle system: Uniform-in-time concentration bounds," Stochastic Processes and their Applications, Elsevier, vol. 156(C), pages 196-225.
    • Handle: RePEc:eee:spapps:v:156:y:2023:i:c:p:196-225
    DOI: 10.1016/j.spa.2022.11.008
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    References listed on IDEAS

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    1. Bayraktar, Erhan & Wu, Ruoyu, 2022. "Stationarity and uniform in time convergence for the graphon particle system," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 532-568.
    2. Bayraktar, Erhan & Wu, Ruoyu, 2021. "Mean field interaction on random graphs with dynamically changing multi-color edges," Stochastic Processes and their Applications, Elsevier, vol. 141(C), pages 197-244.
    3. 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.
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    1. Bayraktar, Erhan & Wu, Ruoyu, 2022. "Stationarity and uniform in time convergence for the graphon particle system," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 532-568.
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