Moduli spaces in string theory, often dubbed Landscapes, are usually of high dimensionality and feature a complicated potential. Is multi-field inflation on such landscapes consistent with current observations by PLANCK? Modeling such landscapes by random potentials offers the opportunity to asses generic features of inflation. Random matrix theory provides a tool (complementing numerical experiments) to address many questions analytically, without requiring a detailed knowledge of the potential, i.e. details of the compactification, due to the feature of universality. Thus, the generic prediction of a landscape in string theory can be put to the test. I will discuss the preference of saddle point inflation in a class of landscapes, commenting on the role of eternal inflation, anthropic arguments and the measure problem within this framework. As an application, I will discuss how current constraints on non-Gaussianities impose bounds on the curvature of the end-of-inflation hyper-surface in this class of models, which in turn imposes constraints on the topography of the landscape.
