Fluctuations study for type-dependent stochastic spin models
Manuel González Navarrete
Tue, Jun 19, 2012
PIMS, University of British Columbia
PIMS-MPrime Summer School in Probability
We study the fluctuations process for the type-dependent stochastic spin models proposed by Fernández et al., which were used to model biological signaling networks. Using the results of Ethier & Kurtz , we analyse the asymmetric basic clock , 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.  S.N. Ethier, T.G. Kurtz, Markov Processes, Characterization and Convergence. Wiley, New York, 1986.  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.  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.
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