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.

Keywords:

• Hydrodynamic limit
• N-urn Ehrenfest model
• moderate deviation
• replacement lemma

Mathematics Subject Classifications:

• 60K35
• 60F10

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Authors are grateful to the financial support from the Fundamental Research Funds for the Central Universities with grant number 2022JBMC039.