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Title: Resolution of a conjecture on majority dynamics: Rapid stabilization in dense random graphs

We study majority dynamics on the binomial random graphG(n, p) withp = d/nand, for some large. In this process, each vertex has a state in {− 1, + 1} and at each round every vertex adopts the state of the majority of its neighbors, retaining its state in the case of a tie. We show that with high probability the process reaches unanimity in at most four rounds. This confirms a conjecture of Benjamini et al.

 
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NSF-PAR ID:
10240499
Author(s) / Creator(s):
 ;  ;  
Publisher / Repository:
Wiley Blackwell (John Wiley & Sons)
Date Published:
Journal Name:
Random Structures & Algorithms
Volume:
57
Issue:
4
ISSN:
1042-9832
Page Range / eLocation ID:
p. 1134-1156
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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