Open Access
January 2008 Stochastic networks with multiple stable points
Nelson Antunes, Christine Fricker, Philippe Robert, Danielle Tibi
Ann. Probab. 36(1): 255-278 (January 2008). DOI: 10.1214/009117907000000105


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.


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Nelson Antunes. Christine Fricker. Philippe Robert. Danielle Tibi. "Stochastic networks with multiple stable points." Ann. Probab. 36 (1) 255 - 278, January 2008.


Published: January 2008
First available in Project Euclid: 28 November 2007

zbMATH: 1130.60086
MathSciNet: MR2370604
Digital Object Identifier: 10.1214/009117907000000105

Primary: 60K25 , 60K35
Secondary: 82B20

Keywords: Energy function , fixed point equations , mean field limit , metastability , stable equilibrium points

Rights: Copyright © 2008 Institute of Mathematical Statistics

Vol.36 • No. 1 • January 2008
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