Astérisque N° 349/2013
Voter model perturbations and reaction diffusion equations
Par : , , Formats :
- Réservation en ligne avec paiement en magasin :
- Indisponible pour réserver et payer en magasin
- Nombre de pages113
- PrésentationBroché
- FormatGrand Format
- Poids0.265 kg
- Dimensions17,5 cm × 24,0 cm × 0,8 cm
- ISBN978-2-85629-355-3
- EAN9782856293553
- Date de parution01/03/2013
- ÉditeurSociété Mathématique de France
Résumé
As applications, we describe the phase diagrams of four systems when the parameters are close to the voter model : (i) a stochastic spatial Lotka-Volterra model of Neuhauser and Pacata, (ii) a model of the evolution of cooperation of Ohtsuki, Hauert, Lieberman, and Nowak, (iii) a continuous time version of the non-linear voter model of Molofsky, Durrett, Dushoff, Griffeath, and Levin, (iv) a voter model in which opinion changes are followed by an exponentially distributed latent period during which voters will not change again.
The first application confirms a conjecture of Cox and Perkins ("Survival and coexistence in stochastic spatial Lotka-Volterra models", 2007) and the second confirms a conjecture of Ohtsuki et al. ("A simple rule for the evolution of cooperation on graphs and social networks", 2006) in the context of certain infinit graphs. An important feature of our general results is that do not require the process to be attractive.