Abstract :
The coupled two-matrix model is studied in the case of one of the matrices belonging to the orthogonal ensemble and the other one belonging to the unitary ensemble, using the Dyson-Schwinger equations or loop equations. The loop equations form an infinite hierarchy which becomes a closed set of algebraic equations in the large-N limit. This allows for the determination of correlation functions of loop operators and the eigenvalue correlators of the model. In particular, we determine the density-density correlators relevant in models of quantum chaos where crossover from one symmetry class to another occurs. The method gives smoothed global correlators.
