2021/11/30 by Danny Nam, Nam, Danny, Allan Sly +3
Energy · Physics and Astronomy · #60G15 #60K35 #82B44 #82D30 #Advanced Chemical Physics Studies #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Metalloenzymes and iron-sulfur proteins #Probability (math.PR) #Spectroscopy and Quantum Chemical Studies
paper · pdf · doi:10.48550/arxiv.2112.00152
openalex publication_date 2021/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Continuing our earlier work in \citenss20a, we study the random regular k-NAE-SAT model in the condensation regime. In \citenss20a, the 1RSB properties of the model were established with positive probability. In this paper, we improve the result to probability arbitrarily close to one. To do so, we introduce a new framework which is the synthesis of two approaches: the small subgraph conditioning and a variance decomposition technique using Doob martingales and discrete Fourier analysis. The main challenge is a delicate integration of the two methods to overcome the difficulty arising from applying the moment method to an unbounded state space.