Majority dynamics on sparse random graphs

Debsoumya Chakraborti, Jeong Han Kim, Joonkyung Lee, Tuan Tran

Research output: Contribution to journalArticlepeer-review


Majority dynamics on a graph (Formula presented.) is a deterministic process such that every vertex updates its (Formula presented.) -assignment according to the majority assignment on its neighbor simultaneously at each step. Benjamini, Chan, O'Donnell, Tamuz and Tan conjectured that, in the Erdős–Rényi random graph (Formula presented.), the random initial (Formula presented.) -assignment converges to a (Formula presented.) -agreement with high probability whenever (Formula presented.). This conjecture was first confirmed for (Formula presented.) for a large constant (Formula presented.) by Fountoulakis, Kang and Makai. Although this result has been reproved recently by Tran and Vu and by Berkowitz and Devlin, it was unknown whether the conjecture holds for (Formula presented.). We break this (Formula presented.) -barrier by proving the conjecture for sparser random graphs (Formula presented.), where (Formula presented.) with a large constant (Formula presented.).

Original languageEnglish
JournalRandom Structures and Algorithms
Publication statusAccepted/In press - 2023

Bibliographical note

Funding Information:
Debsoumya Chakraborti supported by the Institute for Basic Science (IBS‐R029‐C1). Jeong Han Kim supported in part by National Research Foundation of Korea (NRF) Grants funded by the Korean Government (MSIP) (NRF‐2016R1A5A1008055, NRF‐2012R1A2A2A01018585 & 2017R1E1A1A03070701) and by KIAS Individual Grant (CG046001). Joonkyung Lee supported by the Hanyang University research fund (HY‐202100000003086) and the IMSS Research Fellowship. Tuan Tran supported by the Institute for Basic Science (IBS‐R029‐Y1), and the Outstanding Young Talents Program (Overseas) of the National Natural Science Foundation of China.

Funding Information:
Institute for Basic Science, Grant/Award Numbers: IBS‐R029‐C1; IBS‐R029‐Y1; National Research Foundation of Korea, Grant/Award Numbers: NRF‐2012R1A2A2A01018585; NRF‐2016R1A5A1008055; 2017R1E1A1A03070701; KIAS Individual, Grant/Award Number: CG046001; Hanyang University, Grant/Award Number: HY‐202100000003086; University College London: IMSS Research Fellowship, Outstanding Young Talents Program (Overseas) of the National Natural Science Foundation of China Funding information

Publisher Copyright:
© 2023 Wiley Periodicals LLC.

All Science Journal Classification (ASJC) codes

  • Software
  • Mathematics(all)
  • Computer Graphics and Computer-Aided Design
  • Applied Mathematics


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