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Título: | Binary-state dynamics on complex networks: Stochastic pair approximation and beyond |
Autor: | Peralta, Antonio F.; Toral, Raúl CSIC ORCID | Fecha de publicación: | 2020 | Editor: | arXiv | Resumen: | Theoretical approaches to binary-state models on complex networks are generally restricted to infinite size systems, where a set of non-linear deterministic equations is assumed to characterize its dynamics and stationary properties. We develop in this work the stochastic formalism of the different compartmental approaches, these are: approximate master equation (AME), pair approximation (PA) and heterogeneous mean field (HMF), in descending order of accuracy. Using different system-size expansions of a general master equation, we are able to obtain approximate solutions of the fluctuations and finite-size corrections of the global state. On the one hand, far from criticality, the deviations from the deterministic solution are well captured by a Gaussian distribution whose properties we derive, including its correlation matrix and corrections to the average values. On the other hand, close to a critical point there are non-Gaussian statistical features that can be described by the finite-size scaling functions of the models. We show how to obtain the scaling functions departing only from the theory of the different approximations. We apply the techniques for a wide variety of binary-state models in different contexts, such as epidemic, opinion and ferromagnetic models. | Versión del editor: | https://arxiv.org/abs/2004.02791 | URI: | http://hdl.handle.net/10261/218512 |
Aparece en las colecciones: | (IFISC) Artículos |
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