Testing the gaussian expansion method in exactly solvable matrix models

The Gaussian expansion has been developed since early 80s as a powerfulanalytical method, which enables nonperturbative studies of various systemsusing `perturbative' calculations. Recently the method has been used to suggestthat 4d space-time is generated dynamically in a matrix model formulation ofsuperstring theory. Here we clarify the nature of the method by applying it toexactly solvable one-matrix models with various kinds of potential includingthe ones unbounded from below and of the double-well type. We also formulate aprescription to include a linear term in the Gaussian action in a wayconsistent with the loop expansion, and test it in some concrete examples. Wediscuss a case where we obtain two distinct plateaus in the parameter space ofthe Gaussian action, corresponding to different large-N solutions. Thisclarifies the situation encountered in the dynamical determination of thespace-time dimensionality in the previous works.Comment: 30 pages, 15 figures, LaTeX; added references for section