Equilibrium moderate deviations for occupation times of SSEP on regula trees

In this paper, we are concerned with the symmetric simple exclusion process on the regula tree ${\mathbb{T}}^d$ for $d\ge 2$. Our main result gives moderate deviation principles of occupation times of the process starting from an invariant product measure. Two replacement lemmas play key roles in the proof of our main result. To obtain these replacement lemmas, we utilize duality relationships between the symmetric exclusion process and two types of random walks on ${\mathbb{T}}^d$ and ${\left({\mathbb{T}}^d\right)}^2$ respectively.