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Limit behavior of the exponential voter model. (English) Zbl 1230.91157

Summary: We investigate theoretically a voter model or how opinion changes within a community, subject to neighborhood interaction. Under Markov chain modeling, the stationary probability distribution for certain cases is determined in simple analytical form, then its entropy is analyzed.

MSC:

91B80 Applications of statistical and quantum mechanics to economics (econophysics)
60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B43 Percolation
37B15 Dynamical aspects of cellular automata
91D99 Mathematical sociology (including anthropology)
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References:

[1] Agapie, A.; Aus der Fuenten, T., Stationary distribution for a majority voter model, Stochastic Models, 24, 4, 503-512 (2008) · Zbl 1153.60051
[2] Agapie, A.; Mühlenbein, H.; Höns, R., Markov chain analysis for one-dimensional asynchronous cellular automata, Methodology and Computing in Applied Probability, 6, 2, 181-201 (2004) · Zbl 1044.60058
[3] Durrett, R., Lecture Notes on Particle Systems and Percolation (1988), Wadsworth · Zbl 0659.60129
[4] Keller, G., Equilibrium States in Ergodic Theory (1998), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0896.28006
[5] Lambiotte, R.; Redner, S., Dynamics of non-conservative Voters, Europhysics Letters, 82, 18007 (2008)
[6] Liggett, T. M., Interacting Particle Systems (2005), Springer · Zbl 0832.60094
[7] Newman, M. E.J.; Barkema, G. T., Monte Carlo Methods in Statistical Physics (1999), Oxford Univ. Press · Zbl 1012.82019
[8] Oomes, N. A., Emerging markets and persistent inequality in a non-linear voter model, (Griffeath, D.; Moore, C., New Constructions in Cellular Automata (2002), Oxford University Press), 207-229
[9] Slikker, M.; Gilles, R.; Norde, H.; Tijs, S., Directed networks, allocation properties and hierarchy formation, Mathematical Social Science, 49, 55-80 (2005) · Zbl 1118.91029
[10] Wolfram, S., Cellular Automata and Complexity: Collected Papers (1994), Addison-Wesley: Addison-Wesley Reading · Zbl 0823.68003
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