Moderate deviations of generalized $N$-urn Ehrenfest models

TL;DR

This paper establishes a moderate deviation principle for the generalized N-urn Ehrenfest model, extending previous hydrodynamic limit results and employing large deviation techniques.

Contribution

It introduces a moderate deviation principle for the model, building on prior hydrodynamic limit and large deviation results, with a novel application of the replacement lemma.

Findings

Derived a moderate deviation principle from the hydrodynamic limit.

Utilized large deviation principles to prove the replacement lemma.

Extended understanding of fluctuations in the generalized N-urn Ehrenfest model.

Abstract

This paper is a further investigation of the generalized $N$-urn Ehrenfest model introduced in \cite{Xue2020}. A moderate deviation principle from the hydrodynamic limit of the model is derived. The proof of this main result follows a routine procedure introduced in \cite{Kipnis1989}, where a replacement lemma plays the key role. To prove the replacement lemma, the large deviation principle of the model given in \cite{Xue2020} is utilized.