Moderate deviations for traces of words in a mult-matrix model. (English) Zbl 1189.15043

Eichelsbacher, Peter; Sommerauer, Jens

Electron. Commun. Probab. 14, 572-586 (2009).

Summary: 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 Gaussian unitary ensemble. The remarkable strength of high order expansions of the matrix model recently found by A. Guionnet and E. Maurel-Segala [Ann. Probab. 35, No. 6, 2160–2212 (2007; Zbl 1129.15020)] 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 [loc. cit.].

MSC:

15B52	Random matrices (algebraic aspects)
60F05	Central limit and other weak theorems
60F10	Large deviations

Keywords:

random matrices; moderate deviations; map enumeration; traces of words; Gaussian unitary ensemble

Citations:

Zbl 1129.15020