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

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Rybko, Alexander
Shlosman, Senya
Vladimirov, Alexander
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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.
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Mathematical Physics, 82C20, 60J25
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