We prove a moderate deviation principle for traces of words of weakly interacting random matrices defined by a multi-matrix model with a potential being a small perturbation of the GUE. The remarkable strength of high order expansions of the matrix model recently found by Guionnet and Maurel-Segala is the key fact that allows us to develop our result and provides also an alternative proof for a special case of the central limit theorem for traces of words, studied in the article of Guionnet and Maurel-Segala (2006).
"Moderate deviations for traces of words in a mult-matrix model." Electron. Commun. Probab. 14 572 - 586, 2009. https://doi.org/10.1214/ECP.v14-1515