Large deviations for mean field model in Erdos-Renyi graph

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.