Journal
STATISTICS & PROBABILITY LETTERS
Volume 205, Issue -, Pages -Publisher
ELSEVIER
DOI: 10.1016/j.spl.2023.109953
Keywords
Large deviations; Mean-field systems; Erdos-Renyi graph; Grothendieck inequalities
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This paper studies the behavior of a particle systems on an Erdos-Renyi graph under large deviations and establishes the exponential equivalence between the systems and general interacting systems without random graphs. The results provide a foundation for the large deviations theory of particle systems.
In this paper, we study a particle systems (or interacting diffusions) on an Erdos-Renyi graph with the parameter p(N) is an element of (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 Np-N(4) as N -> infinity, 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.
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