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

TL;DR

This paper proves that at low load, mean-field networks behave according to the Poisson Hypothesis, with network equilibration independent of size, contrasting with high load conditions where relaxation times diverge.

Contribution

It establishes that phase transitions do not occur at low load, confirming the Poisson Hypothesis for mean-field networks in this regime.

Findings

Networks equilibrate quickly at low load

Poisson Hypothesis holds at low load

No phase transition occurs at low load

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.