Stochastic networks with multiple stable points

• 成果类型: Article
• 署名作者: Antunes, Nelson; Fricker, Christine; Robert, Philippe; Tibi, Danielle
• 署名单位: Universidade do Algarve; Universite Paris Cite
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117907000000105
• 发表日期: 2008
• 页码: 255-278
• 关键词: markov random-fields; metastability

摘要

This paper analyzes stochastic networks consisting of a set of finite capacity sites where different classes of individuals move according to some routing policy. The associated Markov jump processes are analyzed under a thermodynamic limit regime, that is, when the networks have some symmetry properties and when the number of nodes goes to infinity. An intriguing stability property is proved: under some conditions on the parameters, it is shown that, in the limit, several stable equilibrium points coexist for the empirical distribution. The key ingredient of the proof of this property is a dimension reduction achieved by the introduction of two energy functions and a convenient mapping of their local minima and saddle points. Networks with a unique equilibrium point are also presented.