[Choix idiosyncrasiques et erratiques : non-linéarité et transitions induites par le vieillissement dans le modèle de l'électeur aléatoire]
Nous considérons la transition grégaire/non grégaire causée par des choix idiosyncrasiques ou une imitation imparfaite dans le contexte du modèle de Kirman pour les marchés financiers ou, de façon équivalente, du modèle de l'électeur aléatoire pour la formation de l'opinion. Dans ces modèles originaux, il s'agit d'une transition de taille finie qui disparaît pour un grand nombre d'agents. Nous montrons comment l'introduction de deux mécanismes différents rend cette transition robuste et bien définie. Un premier mécanisme est celui des interactions non linéaires entre agents tenant compte de l'effet non linéaire des majorités locales. La deuxième est le vieillissement, de sorte que plus un agent a été longtemps dans un état donné, plus il devient réticent à changer d'état.
We consider the herding-to-non-herding transition caused by idiosyncratic choices or imperfect imitation in the context of the Kirman Model for financial markets, or equivalently the Noisy Voter Model for opinion formation. In these original models, this is a finite-size transition that disappears for a large number of agents. We show how the introduction of two different mechanisms makes this transition robust and well defined. A first mechanism is nonlinear interactions among agents taking into account the nonlinear effect of local majorities. The second one is aging, so that the longer an agent has been in a given state the more reluctant she becomes to change state.
Mot clés : Dynamique des opinions, Modèle de l'électeur aléatoire, Vieillissement, Transition de phase
@article{CRPHYS_2019__20_4_262_0,
author = {Oriol Artime and Adri\'an Carro and Antonio F. Peralta and Jos\'e J. Ramasco and Maxi San Miguel and Ra\'ul Toral},
title = {Herding and idiosyncratic choices: {Nonlinearity} and aging-induced transitions in the noisy voter model},
journal = {Comptes Rendus. Physique},
pages = {262--274},
publisher = {Elsevier},
volume = {20},
number = {4},
year = {2019},
doi = {10.1016/j.crhy.2019.05.003},
language = {en},
}
TY - JOUR AU - Oriol Artime AU - Adrián Carro AU - Antonio F. Peralta AU - José J. Ramasco AU - Maxi San Miguel AU - Raúl Toral TI - Herding and idiosyncratic choices: Nonlinearity and aging-induced transitions in the noisy voter model JO - Comptes Rendus. Physique PY - 2019 SP - 262 EP - 274 VL - 20 IS - 4 PB - Elsevier DO - 10.1016/j.crhy.2019.05.003 LA - en ID - CRPHYS_2019__20_4_262_0 ER -
%0 Journal Article %A Oriol Artime %A Adrián Carro %A Antonio F. Peralta %A José J. Ramasco %A Maxi San Miguel %A Raúl Toral %T Herding and idiosyncratic choices: Nonlinearity and aging-induced transitions in the noisy voter model %J Comptes Rendus. Physique %D 2019 %P 262-274 %V 20 %N 4 %I Elsevier %R 10.1016/j.crhy.2019.05.003 %G en %F CRPHYS_2019__20_4_262_0
Oriol Artime; Adrián Carro; Antonio F. Peralta; José J. Ramasco; Maxi San Miguel; Raúl Toral. Herding and idiosyncratic choices: Nonlinearity and aging-induced transitions in the noisy voter model. Comptes Rendus. Physique, Volume 20 (2019) no. 4, pp. 262-274. doi : 10.1016/j.crhy.2019.05.003. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2019.05.003/
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