Majority dynamics and the median process: Connections, convergence and some new conjectures

Gideon Amir, Rangel Baldasso, Nissan Beilin

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

We consider the median dynamics process in general graphs. In this model, each vertex has an independent initial opinion uniformly distributed in the interval [0,1] and, with rate one, updates its opinion to coincide with the median of its neighbors. This process provides a continuous analog of binary majority dynamics. We deduce properties of median dynamics through this connection and raise new conjectures regarding the behavior of majority dynamics on general graphs. We also prove these conjectures on some graphs where majority dynamics has a simple description.

Original languageEnglish
Pages (from-to)437-458
Number of pages22
JournalStochastic Processes and their Applications
Volume155
DOIs
StatePublished - Jan 2023

Bibliographical note

Publisher Copyright:
© 2022

Funding

This work was supported by the Israel Science Foundation through grant 575/16 and by the German Israeli Foundation through grant I-1363-304.6/2016 . We thank Idan Alter for providing us with the simulations in Section 5 .

FundersFunder number
German Israeli FoundationI-1363-304.6/2016
Israel Science Foundation575/16

    Keywords

    • Majority dynamics
    • Median process

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