The random $k$-SAT Gibbs uniqueness threshold revisited
Discrete Mathematics
2025-11-19 v2 Combinatorics
Probability
Abstract
We prove that for any for clause/variable ratios up to the Gibbs uniqueness threshold of the corresponding Galton-Watson tree, the number of satisfying assignments of random -SAT formulas is given by the `replica symmetric solution' predicted by physics methods [Monasson, Zecchina: Phys. Rev. Lett. (1996)]. Furthermore, while the Gibbs uniqueness threshold is still not known precisely for any , we derive new lower bounds on this threshold that improve over prior work [Montanari and Shah: SODA (2007)].The improvement is significant particularly for small .
Cite
@article{arxiv.2506.01359,
title = {The random $k$-SAT Gibbs uniqueness threshold revisited},
author = {Arnab Chatterjee and Amin Coja-Oghlan and Catherine Greenhill and Vincent Pfenninger and Maurice Rolvien and Pavel Zakharov and Kostas Zampetakis},
journal= {arXiv preprint arXiv:2506.01359},
year = {2025}
}