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

2008/11/21 by Alexander Rybko, Rybko, Alexander, Senya Shlosman +3
Physics and Astronomy · #60J25 #82C20 #Advanced Thermodynamics and Statistical Mechanics #Complex Network Analysis Techniques #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.0811.3577

openalex publication_date 2008/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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