Absence of Breakdown of the Poisson Hypothesis. I. Closed Networks at Low Load

A.N. Rybko, S. Shlosman, A. Vladimirov

2010, v.16, №2, 267-285

ABSTRACT

We prove that the general mean-field type networks at low load behave in accordance with the Poisson Hypothesis. That means that the network equilibrates in time independent of its size. This is a 'high-temperature' counterpart of our earlier result, where we have shown that at high load the relaxation time can diverge with the size of the network ('low-temperature'). In other words, the phase transitions in the networks can happen at high load, but cannot take place at low load.

Keywords: coupled dynamical systems,non-linear Markov processes,stableattractor,phase transition,long-range order

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