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arXiv · 2610.39545

The Mézard-Parisi formula

Dmitry Panchenko
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Abstract

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.

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Dmitry Panchenko. 2026-10-29. The Mézard-Parisi formula. https://arxiv.org/abs/2610.39545

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