On the exit probability of the one dimensional q-voter model. Analytical results and simulations for large networks. (2013)
- Authors:
- Autor USP: PRADO, CARMEN PIMENTEL CINTRA DO - IF
- Unidade: IF
- Subjects: PROCESSOS ESTOCÁSTICOS; SIMULAÇÃO; ANÁLISE DE SÉRIES TEMPORAIS
- Language: Inglês
- Abstract: We discuss the exit probability of the one dimensional q-voter model and present tools to obtain estimates about this probability both through simulations in large networks (around 107 sites) and analyticaly in the limit where the network is infinetely large. We argue that the result E(ρ) = ρ q ρq+(1−ρ) q , that was found in 3 previous works (2008 EPL 82 18006 and 2008 EPL 82 18007, for the case q = 2 and 2011 PRE 84 031117, for q > 2) using small networks (around 103 sites), is a good approximation, but there are noticeable deviations for larger system sizes. We also show that, under some simple and intuitive hypothesis, the exit probability must obey the inequality, ρ q ρq+(1−ρ) ≤ E(ρ) ≤ ρ ρ+(1−ρ) q , in the infinite size limit. We believe this settles in the negative the suggestion made (2011 EPL 95 48005) that this result would be a finite size effect, with the exit probability actualy being a step function. We also show how the result, that the exit probability cannot be a step function, can be reconciled with the Galam unified frame, which was also a source of controversy.
- Imprenta:
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ABNT
TIMPANARO, André M e PRADO, Carmen Pimentel Cintra do. On the exit probability of the one dimensional q-voter model. Analytical results and simulations for large networks. . São Paulo: Instituto de Física, Universidade de São Paulo. Disponível em: http://lanl.arxiv.org/pdf/1312.2269v1.pdf. Acesso em: 16 maio 2024. , 2013 -
APA
Timpanaro, A. M., & Prado, C. P. C. do. (2013). On the exit probability of the one dimensional q-voter model. Analytical results and simulations for large networks. São Paulo: Instituto de Física, Universidade de São Paulo. Recuperado de http://lanl.arxiv.org/pdf/1312.2269v1.pdf -
NLM
Timpanaro AM, Prado CPC do. On the exit probability of the one dimensional q-voter model. Analytical results and simulations for large networks. [Internet]. 2013 ;[citado 2024 maio 16 ] Available from: http://lanl.arxiv.org/pdf/1312.2269v1.pdf -
Vancouver
Timpanaro AM, Prado CPC do. On the exit probability of the one dimensional q-voter model. Analytical results and simulations for large networks. [Internet]. 2013 ;[citado 2024 maio 16 ] Available from: http://lanl.arxiv.org/pdf/1312.2269v1.pdf - Criticalidade de auto-organizada no modelo OFC
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