One-step replica symmetry breaking of random regular NAE-SAT II
Abstract
Continuing our earlier work in \cite{nss20a}, we study the random regular k-NAE-SAT model in the condensation regime. In \cite{nss20a}, 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.
Keywords
Cite
@article{arxiv.2112.00152,
title = {One-step replica symmetry breaking of random regular NAE-SAT II},
author = {Danny Nam and Allan Sly and Youngtak Sohn},
journal= {arXiv preprint arXiv:2112.00152},
year = {2023}
}
Comments
57 pages, 1 figure. Accepted to Communications in Mathematical Physics. arXiv admin note: text overlap with arXiv:2011.14270