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**Harvard**

Hirscher, T. (2014) *The Deffuant model on Z with higher-dimensional opinion spaces*.

** BibTeX **

@article{

Hirscher2014,

author={Hirscher, Timo},

title={The Deffuant model on Z with higher-dimensional opinion spaces},

journal={Latin American Journal of Probability and Mathematical Statistics},

issn={1980-0436},

volume={XI},

issue={2},

pages={409-444},

abstract={When it comes to the mathematical modelling of social interaction patterns, a number of different models have emerged and been studied over the last decade, in which individuals randomly interact on the basis of an underlying graph structure and share their opinions. A prominent example of the so-called bounded confidence models is the one introduced by Deffuant et al.: Two neighboring individuals will only interact if their opinions do not differ by more than a given threshold θ. We consider this model on the line graph Z and extend the results
that have been achieved for the model with real-valued opinions by considering vector-valued opinions and general metrics measuring the distance between two opinion values. As in the univariate case there turns out to exist a critical value θ_c for θ at which a phase transition in the long-term behavior takes place, but θ_c depends on the initial distribution in a more intricate way than in the univariate
case.},

year={2014},

keywords={Deffuant model, consensus formation, vector-valued opinions.},

}

** RefWorks **

RT Journal Article

SR Electronic

ID 206608

A1 Hirscher, Timo

T1 The Deffuant model on Z with higher-dimensional opinion spaces

YR 2014

JF Latin American Journal of Probability and Mathematical Statistics

SN 1980-0436

VO XI

IS 2

SP 409

OP 444

AB When it comes to the mathematical modelling of social interaction patterns, a number of different models have emerged and been studied over the last decade, in which individuals randomly interact on the basis of an underlying graph structure and share their opinions. A prominent example of the so-called bounded confidence models is the one introduced by Deffuant et al.: Two neighboring individuals will only interact if their opinions do not differ by more than a given threshold θ. We consider this model on the line graph Z and extend the results
that have been achieved for the model with real-valued opinions by considering vector-valued opinions and general metrics measuring the distance between two opinion values. As in the univariate case there turns out to exist a critical value θ_c for θ at which a phase transition in the long-term behavior takes place, but θ_c depends on the initial distribution in a more intricate way than in the univariate
case.

LA eng

LK http://alea.impa.br/articles/v11/11-18.pdf

LK http://publications.lib.chalmers.se/records/fulltext/206608/local_206608.pdf

OL 30