The Mézard-Parisi formula

This paper proves the Mézard-Parisi formula for the free energy of random K-sat and diluted p-spin models with even p, completing an approach developed in earlier work of the author and collaborators. The upper bound was established by Franz and Leone. Here the matching lower bound is proved for a general class of diluted models under symmetry and integrability assumptions. The main new contribution is a proof of an approximate form of the Mézard-Parisi reproducibility hypothesis without assuming that the overlap distribution has finite support.