We prove the Large Deviation Principle for the empirical process in a system of locally interacting Brownian motions in the nonequilibrium dynamic. Such a phenomenon has been proven only for two lattice systems: the symmetric simple exclusion process and zero-range process. Therefore, we have achieved the third result in this context and moreover the first result for the diffusion-type interacting particle system.
Large deviations for flows of interacting Brownian motions
Interacting Brownian motions in infinite dimensions with logarithmic interaction potentials
Asymptotic description of stochastic neural networks. I - existence of a Large Deviation Principle
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