Absence of Breakdown of the Poisson Hypothesis I. Closed Networks at Low Load
Mathematical Physics
2008-11-24 v1 math.MP
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
Cite
@article{arxiv.0811.3577,
title = {Absence of Breakdown of the Poisson Hypothesis I. Closed Networks at Low Load},
author = {Alexander Rybko and Senya Shlosman and Alexander Vladimirov},
journal= {arXiv preprint arXiv:0811.3577},
year = {2008}
}