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Title: One-Step Replica Symmetry Breaking of Random Regular NAE-SAT II
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 regulark-nae-satmodel 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.  more » « less
Award ID(s):
1954337
PAR ID:
10492211
Author(s) / Creator(s):
; ;
Publisher / Repository:
Springer Science + Business Media
Date Published:
Journal Name:
Communications in Mathematical Physics
Volume:
405
Issue:
3
ISSN:
0010-3616
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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