Large deviations for interacting diffusions with path-dependent McKean–Vlasov limit

We consider a mean-field system of path-dependent stochastic interacting diffusions in random media over finite time window. The interaction term is given as function the empirical measure and allowed to be non-linear path dependent. prove that sequence measures full trajectories satisfies large deviation principle with explicit rate function. minimizer characterized McKean-Vlasov diffusion associated system. As corollary, we obtain strong law numbers for measures. proof based on decoupling technique by associating convenient family product To illustrate, apply our results delayed Kuramoto model SDE version Galves-L\"ocherbach model.