# Correlation function of partition functions

In this paper the authors study the correlation function of partition functions defined by

$$\langle Z(\beta_1) \ldots Z(\beta_n) \rangle = \frac{1}{\mathcal{Z}}\int \mathrm{d}H \, \mathrm{e}^{-L \, \mathrm{Tr} \, V(H)} Z(\beta_1) \ldots Z(\beta_n)$$

where

$$Z(\beta) \equiv \mathrm{Tr} \, \mathrm{e}^{- \beta H}$$ and

$$\mathcal{Z} \equiv \int \mathrm{d} H \, \mathrm{e}^{-L \, \mathrm{Tr} \, V(H)}.$$

$$H$$ is a Hermitian matrix.

How do we physically interpret these correlation functions? They call $$Z(\beta)$$ an observable; what experiment would we conduct to measure it? Please feel free to explain based on any physical system described in this way, the JT gravity description is incidental to this question. Thanks!