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Accuracy criterion for mean field approximations of Markov processes on hypergraphs

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  • Keliger, Dániel
  • Horváth, Illés

Abstract

We provide error bounds for the N-intertwined mean-field approximation (NIMFA) for local density-dependent Markov population processes with a well-distributed underlying network structure showing NIMFA being accurate when a typical vertex has many neighbors. The result justifies some of the most common approximations used in epidemiology, statistical physics and opinion dynamics literature under certain conditions. We allow interactions between more than 2 individuals, and an underlying hypergraph structure accordingly.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:609:y:2023:i:c:s0378437122009281
    DOI: 10.1016/j.physa.2022.128370
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    References listed on IDEAS

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    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. Iacopo Iacopini & Giovanni Petri & Alain Barrat & Vito Latora, 2019. "Simplicial models of social contagion," Nature Communications, Nature, vol. 10(1), pages 1-9, December.
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    Cited by:

    1. Keliger, Dániel, 2024. "Universality of SIS epidemics starting from small initial conditions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 644(C).

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