Smoothed Correlators For Symmetric Double-Well Matrix Models: Some Puzzles and Resolutions

Some puzzles which arise in matrix models with multiple cuts are presented. They are present in the smoothed eigenvalue correlators of these models. First a method is described to calculate smoothed eigenvalue correlators in random matrix models with eigenvalues distributed in a single-cut, previous known results are reproduced. The method is extended to symmetric two-cut random matrix models. The correlators are written in a form suitable for application to mesoscopic systems. Connections are made with the smooth correlators derived using the Orthogonal Polynomial (OP) method. A few interesting observations are made regarding even and odd density-density correlators and cross-over correlators in $Z_2$ symmetric random matrix models.