Fluctuations study for type-dependent stochastic spin models

We study the fluctuations process for the type-dependent stochastic spin models proposed by Fernández et al.[2], which were used to model biological signaling networks. Using the results of Ethier & Kurtz [1], we analyse the asymmetric basic clock [3], a extension for the simplest cyclic-interaction module, that provides the basic functionality of generating oscillations. Particularly, we apply the central limit theorem for fluctuations process; the dynamics of this limit process is our aim. References. [1] S.N. Ethier, T.G. Kurtz, Markov Processes, Characterization and Convergence. Wiley, New York, 1986. [2] R. Fernandez, L.R. Fontes, E.J. Neves, Density-Profile Processes Describing Biological Signaling Networks: Almost Sure Convergence to Deterministic Trajectories. J Stat Phys (2009) 136: 875-901. [3] M.A. González Navarrete, Sistemas de partículas interagentes dependentes de tipo e aplicaçoes ao estudo de redes de sinalizaçao biológica. Master thesis, Instituto de Matemática e Estatística USP, 2011.