Large Deviation Principle For Finite-State Mean Field Interacting   Particle Systems
  We establish a large deviation principle for the empirical measure process associated with a general class of finite-state mean field interacting particle systems with Lipschitz continuous transition rates that satisfy a certain ergodicity condition. The approach is based on a variational representation for functionals of a Poisson random measure. Under an appropriate strengthening of the ergodicity condition, we also prove a locally uniform large deviation principle. The main novelty is that more than one particle is allowed to change its state simultaneously, and so a standard approach to the proof based on a change of measure with respect to a system of independent particles is not possible. The result is shown to be applicable to a wide range of models arising from statistical physics, queueing systems and communication networks. Along the way, we establish a large deviation principle for a class of jump Markov processes on the simplex, whose rates decay to zero as they approach the boundary of the domain. This result may be of independent interest. 
Paul Dupuis, Kavita Ramanan, Wei Wu
math.PR