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One-Step Replica Symmetry Breaking of Random Regular NAE-SAT II
Ist Teil von
Communications in mathematical physics, 2024-03, Vol.405 (3)
Ort / Verlag
Berlin/Heidelberg: Springer Berlin Heidelberg
Erscheinungsjahr
2024
Link zum Volltext
Quelle
Alma/SFX Local Collection
Beschreibungen/Notizen
Continuing our earlier work in Nam et al. (One-step replica symmetry breaking of random regular NAE-SAT I,
arXiv:2011.14270
, 2020), we study the random regular
k
-
nae-sat
model in the condensation regime. In Nam et al. (2020), the (1
rsb
) 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.