Fluctuations study for type-dependent stochastic spin models

PIMS-MPrime Summer School in Probability

授课人:Manuel Gonz谩lez Navarrete

机构:Pacific Institute for the Mathematical Sciences(PIMS)

关键词: Scientific;    Mathematics;    Probability;    Fluctuations Process;   

加拿大|英语

【 摘 要 】

We study the fluctuations process for the type-dependent stochastic spin models proposed by Fern谩ndez 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. Gonz谩lez Navarrete, Sistemas de part铆culas interagentes dependentes de tipo e aplica?oes ao estudo de redes de sinaliza?ao biol贸gica. Master thesis, Instituto de Matem谩tica e Estat铆stica USP, 2011.

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