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arXiv · 2112.00152

One-step replica symmetry breaking of random regular NAE-SAT II

Danny Nam·Allan Sly·Youngtak Sohn
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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.

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BibTeXRIS

Danny Nam, Allan Sly, Youngtak Sohn. 2021-11-30. One-step replica symmetry breaking of random regular NAE-SAT II. https://arxiv.org/abs/2112.00152

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