  We present a theory for the pseudo-gap state recently observed at the
LaAlO3/SrTiO3 interface, based on superconducting islands embedded in a
metallic background. Superconductivity within each island is BCS-like, and the
local critical temperatures are randomly distributed, some of them necessarily
exceeding the critical temperature for global percolation to the zero
resistance state. Consequently, tunneling spectra display a suppression of the
density of states and coherence peaks already well above the percolative
transition. This model of inhomogeneous superconductivity accounts well for the
experimental tunneling spectra. The temperature dependence of the spectra
suggests that a sizable fraction of the metallic background becomes
superconducting by proximity effect when the temperature is lowered.
