One-Step Replica Symmetry Breaking of Random Regular NAE-SAT II
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220_2023_Article_4868.pdf
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1001.74 KB
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Checksum (MD5)
915ee46ba2e467814924c0cff81b35f4
Author(s)
Nam, Danny
Sly, Allan
Sohn, Youngtak
Date Issued
February 23, 2024
Publisher
Springer Science and Business Media LLC
Citation
Nam, D., Sly, A. & Sohn, Y. One-Step Replica Symmetry Breaking of Random Regular NAE-SAT II. Commun. Math. Phys. 405, 61 (2024).
Version
Final published version
Abstract
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.
Subjects
Mathematical Physics
Statistical and Nonlinear Physics
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s00220-023-04868-6
