TY - JOUR
T1 - One-Step Replica Symmetry Breaking of Random Regular NAE-SAT II
AU - Nam, Danny
AU - Sly, Allan
AU - Sohn, Youngtak
N1 - Publisher Copyright:
© The Author(s) 2024.
PY - 2024/3
Y1 - 2024/3
N2 - 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 (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.
AB - 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 (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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U2 - 10.1007/s00220-023-04868-6
DO - 10.1007/s00220-023-04868-6
M3 - Article
AN - SCOPUS:85187254751
SN - 0010-3616
VL - 405
JO - Communications In Mathematical Physics
JF - Communications In Mathematical Physics
IS - 3
M1 - 61
ER -