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

11/30/2021

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by   Danny Nam, et al.

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Continuing our earlier work in <cit.>, we study the random regular k-NAE-SAT model in the condensation regime. In <cit.>, 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.