  In the previous paper, the authors pointed out correspondence between a
supersymmetric double-well matrix model and two-dimensional type IIA
superstring theory on a Ramond-Ramond background from the viewpoint of symmetry
and spectrum. This was confirmed by agreement between planar correlation
functions in the matrix model and tree-level amplitudes in the superstring
theory. In order to investigate the correspondence further, in this paper we
compute correlation functions to all order of genus expansion in the double
scaling limit of the matrix model. One-point functions of operators protected
by supersymmetry terminate at some finite order, whereas those of unprotected
operators yield non-Borel summable series. The behavior of the latter is
characteristic in string perturbation series, providing further evidence that
the matrix model describes a string theory. Moreover, instanton corrections to
the planar one-point functions are also computed, and universal logarithmic
scaling behavior is found for non-supersymmetric operators.
