Large deviations for mean field model in Erdős–Rényi graph

Yunshi Gao

Statistics & Probability Letters, 2024, vol. 205, issue C

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.

Keywords: Large deviations; Mean-field systems; Erdős–Rényi graph; Grothendieck inequalities (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spl.2023.109953

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