Moderate deviations of generalized N-urn Ehrenfest models

Abstract

This paper is a further investigation of the generalized N-urn Ehrenfest model introduced in Xue [Hydrodynamics of the generalized N-urn Ehrenfest model, Potential Anal. 2022. Online. Available at https://rdcu.be/cFzrj]. A moderate deviations principle from the hydrodynamic limit of the model is derived. The proof of this main result follows an exponential martingale approach introduced in C. Kipnis et al. [Hydrodynamics and large deviation for simple exclusion processes, Commun. Pure Appl. Math. 42 (1989), pp. 115–137], where a replacement lemma plays the key role. To prove the replacement lemma, the large deviations principle of the model given in Xue [Hydrodynamics of the generalized N-urn Ehrenfest model, Potential Anal. 2022. Online. Available at https://rdcu.be/cFzrj] is utilized. As applications of our main result, we further give moderate deviations of hitting times of our process and moderate deviations of our process at given moments.