Probability of Vacuum Stability in Type IIB Multi-K\"ahler Moduli Models
  We study the probability that all eigenvalues of the moduli mass matrix at
extremal points are positive in concrete multi-K\"ahler moduli models of type
IIB string theory compactifications in the large volume regime. Our analysis is
motivated by the open question if vacua which are uplifted to de Sitter remain
stable. We derive a simple analytical condition for the mass matrix to be
positive definite, and estimate the corresponding probability in a
supersymmetric moduli stabilization model along the lines of KKLT and a
non-supersymmetric Large Volume Scenario type of model, given a reasonable
range of compactification parameters. Under identical conditions, the
probability for the supersymmetric model is moderately higher than that of the
Large Volume Scenario type model.
