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Large deviations for mean field model in Erdős–Rényi graph

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  • Gao, Yunshi

Abstract

In this paper, we study a particle systems (or interacting diffusions) on an Erdős–Rényi graph with the parameter pN∈(0,1] that behaves like a mean-field system up to large deviations. Our aim is to establish the large deviations for the empirical measure process of particle systems under the condition NpN4→∞ as N→∞, where N is the number of particles. The result is obtained by proving the exponential equivalence between our systems and general interacting systems without random graphs. The multilinear extensions of Grothendieck inequality play a crucial role in our proof.

Suggested Citation

  • Gao, Yunshi, 2024. "Large deviations for mean field model in Erdős–Rényi graph," Statistics & Probability Letters, Elsevier, vol. 205(C).
    • Handle: RePEc:eee:stapro:v:205:y:2024:i:c:s0167715223001773
    DOI: 10.1016/j.spl.2023.109953
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    References listed on IDEAS

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    1. 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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