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

Gideon Amir; Rangel Baldasso; Nissan Beilin

doi:10.1016/j.spa.2022.10.015

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

Gideon Amir, Rangel Baldasso, Nissan Beilin

Department of Mathematics

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

1 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 language	English
Pages (from-to)	437-458
Number of pages	22
Journal	Stochastic Processes and their Applications
Volume	155
DOIs	https://doi.org/10.1016/j.spa.2022.10.015
State	Published - Jan 2023

Bibliographical note

Funding Information:
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 .

Publisher Copyright:
© 2022

Keywords

Majority dynamics
Median process

Access to Document

10.1016/j.spa.2022.10.015

Cite this

@article{d54df4db5078434b9eaeb275f326317e,

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

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.",

keywords = "Majority dynamics, Median process",

author = "Gideon Amir and Rangel Baldasso and Nissan Beilin",

note = "Publisher Copyright: {\textcopyright} 2022",

year = "2023",

month = jan,

doi = "10.1016/j.spa.2022.10.015",

language = "אנגלית",

volume = "155",

pages = "437--458",

journal = "Stochastic Processes and their Applications",

issn = "0304-4149",

publisher = "Elsevier",

}

TY - JOUR

T1 - Majority dynamics and the median process

T2 - Connections, convergence and some new conjectures

AU - Amir, Gideon

AU - Baldasso, Rangel

AU - Beilin, Nissan

PY - 2023/1

Y1 - 2023/1

N2 - 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.

AB - 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.

KW - Majority dynamics

KW - Median process

UR - http://www.scopus.com/inward/record.url?scp=85141928970&partnerID=8YFLogxK

U2 - 10.1016/j.spa.2022.10.015

DO - 10.1016/j.spa.2022.10.015

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85141928970

SN - 0304-4149

VL - 155

SP - 437

EP - 458

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

ER -

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

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this