Fixation and Consensus Times on a Network: A Unified Approach

G. J. Baxter; Richard Blythe; A. J. McKane

doi:10.1103/PhysRevLett.101.258701

Fixation and Consensus Times on a Network: A Unified Approach

G. J. Baxter, Richard Blythe, A. J. McKane

School of Physics and Astronomy

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

Abstract / Description of output

We investigate a set of stochastic models of biodiversity, population genetics, language evolution, and opinion dynamics on a network within a common framework. Each node has a state 0 < x(i)< 1 with interactions specified by strengths m(ij). For any set of m(ij), we derive an approximate expression for the mean time to reach fixation or consensus (all x(i)=0 or 1). Remarkably, in a case relevant to language change, this time is independent of the network structure.

Original language	English
Article number	258701
Pages (from-to)	-
Number of pages	4
Journal	Physical Review Letters
Volume	101
Issue number	25
DOIs	https://doi.org/10.1103/PhysRevLett.101.258701
Publication status	Published - 19 Dec 2008

Access to Document

10.1103/PhysRevLett.101.258701

Cite this

@article{ac3355bd639f426cafacae7c82f737ce,

title = "Fixation and Consensus Times on a Network: A Unified Approach",

abstract = "We investigate a set of stochastic models of biodiversity, population genetics, language evolution, and opinion dynamics on a network within a common framework. Each node has a state 0 < x(i)< 1 with interactions specified by strengths m(ij). For any set of m(ij), we derive an approximate expression for the mean time to reach fixation or consensus (all x(i)=0 or 1). Remarkably, in a case relevant to language change, this time is independent of the network structure.",

author = "Baxter, {G. J.} and Richard Blythe and McKane, {A. J.}",

year = "2008",

month = dec,

day = "19",

doi = "10.1103/PhysRevLett.101.258701",

language = "English",

volume = "101",

pages = "--",

journal = "Physical Review Letters",

issn = "0031-9007",

publisher = "American Physical Society",

number = "25",

}

TY - JOUR

T1 - Fixation and Consensus Times on a Network: A Unified Approach

AU - Baxter, G. J.

AU - Blythe, Richard

AU - McKane, A. J.

PY - 2008/12/19

Y1 - 2008/12/19

N2 - We investigate a set of stochastic models of biodiversity, population genetics, language evolution, and opinion dynamics on a network within a common framework. Each node has a state 0 < x(i)< 1 with interactions specified by strengths m(ij). For any set of m(ij), we derive an approximate expression for the mean time to reach fixation or consensus (all x(i)=0 or 1). Remarkably, in a case relevant to language change, this time is independent of the network structure.

AB - We investigate a set of stochastic models of biodiversity, population genetics, language evolution, and opinion dynamics on a network within a common framework. Each node has a state 0 < x(i)< 1 with interactions specified by strengths m(ij). For any set of m(ij), we derive an approximate expression for the mean time to reach fixation or consensus (all x(i)=0 or 1). Remarkably, in a case relevant to language change, this time is independent of the network structure.

UR - http://www.scopus.com/inward/record.url?scp=58149234881&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.101.258701

DO - 10.1103/PhysRevLett.101.258701

M3 - Article

SN - 0031-9007

VL - 101

SP - -

JO - Physical Review Letters

JF - Physical Review Letters

IS - 25

M1 - 258701

ER -

Fixation and Consensus Times on a Network: A Unified Approach

Abstract / Description of output

Access to Document

Other files and links

Fingerprint

Cite this