In this note, we study the Gaussian fluctuations of the edge occupation measure for a reversible Markov chain and give a nice description of the covariance matrix. Then we give some large deviations results concerning this occupation measure.
"Edge Occupation Measure for a Reversible Markov Chain." Electron. Commun. Probab. 4 87 - 90, 1999. https://doi.org/10.1214/ECP.v4-1009