Majority dynamics on sparse random graphs

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

doi:10.1002/rsa.21139

Majority dynamics on sparse random graphs

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

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Journal	Random Structures and Algorithms
DOIs	https://doi.org/10.1002/rsa.21139
Publication status	Accepted/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

Access to Document

10.1002/rsa.21139

Cite this

@article{5f2244ce5f654962b9c88307cd29fea0,

title = "Majority dynamics on sparse random graphs",

abstract = "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 Erd{\H o}s–R{\'e}nyi 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.).",

author = "Debsoumya Chakraborti and {Han Kim}, Jeong and Joonkyung Lee and Tuan Tran",

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: {\textcopyright} 2023 Wiley Periodicals LLC.",

year = "2023",

doi = "10.1002/rsa.21139",

language = "English",

journal = "Random Structures and Algorithms",

issn = "1042-9832",

publisher = "John Wiley and Sons Ltd",

}

TY - JOUR

T1 - Majority dynamics on sparse random graphs

AU - Chakraborti, Debsoumya

AU - Han Kim, Jeong

AU - Lee, Joonkyung

AU - Tran, Tuan

N1 - 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.

PY - 2023

Y1 - 2023

N2 - 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.).

AB - 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.).

UR - http://www.scopus.com/inward/record.url?scp=85147290102&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85147290102&partnerID=8YFLogxK

U2 - 10.1002/rsa.21139

DO - 10.1002/rsa.21139

M3 - Article

AN - SCOPUS:85147290102

SN - 1042-9832

JO - Random Structures and Algorithms

JF - Random Structures and Algorithms

ER -

Majority dynamics on sparse random graphs

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this