Probabilities in the Arkani-Hamed-Dimopolous-Kachru landscape

In a previous paper, we found that in the context of the string theory 'discretuum' proposed by Bousso and Polchinski, the cosmological constant probability distribution varies wildly. However, the successful anthropic predictions of the cosmological constant depend crucially on the assumption of a flat prior distribution. We conjectured that the staggered character of our Bousso Polchinski distribution will arise in any landscape model which generates a dense spectrum of low-energy constants from a wide distribution of states in the parameter space of the fundamental theory. Here we calculate the volume distribution for Lambda in the simpler Arkani-Hamed-Dimopolous-Kachru landscape model, and indeed this conjecture is borne out.