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Particle Systems with Local Interactions via Hitting Times and Cascades on Graphs

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  • Yucheng Guo
  • Qinxin Yan

Abstract

We introduce a family of particle systems on sparse graphs where local interactions occur via hitting times, providing a dynamic and tractable model for default cascades in large sparsely-connected financial networks. Building on the framework of Lacker, Ramanan and Wu (2023), we extend convergence theory to systems with singular interactions, capturing the abrupt and discontinuous nature of systemic events. We establish conditions for well-posedness through a minimality principle and connect fragility to dynamic percolation thresholds. Our analysis demonstrates continuity of the joint law of defaults with respect to local graph convergence, establishes convergence of empirical distributions, and characterizes the default time distribution in tree-like networks. This framework offers a rigorous and flexible foundation for modeling systemic risk in evolving financial systems, featuring continuous-time dynamics, heterogeneous and local interactions, and instantaneous default cascades.

Suggested Citation

  • Yucheng Guo & Qinxin Yan, 2025. "Particle Systems with Local Interactions via Hitting Times and Cascades on Graphs," Papers 2505.18448, arXiv.org, revised Mar 2026.
    • Handle: RePEc:arx:papers:2505.18448
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    References listed on IDEAS

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    1. Ben Hambly & Andreas Søjmark, 2019. "An SPDE model for systemic risk with endogenous contagion," Finance and Stochastics, Springer, vol. 23(3), pages 535-594, July.
    2. Konstantinos Spiliopoulos & Jia Yang, 2019. "Network Effects in Default Clustering for Large Systems," Applied Mathematical Finance, Taylor & Francis Journals, vol. 26(6), pages 523-582, November.
    3. Larry Eisenberg & Thomas H. Noe, 2001. "Systemic Risk in Financial Systems," Management Science, INFORMS, vol. 47(2), pages 236-249, February.
    4. Hamed Amini & Rama Cont & Andreea Minca, 2016. "Resilience To Contagion In Financial Networks," Mathematical Finance, Wiley Blackwell, vol. 26(2), pages 329-365, April.
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