Phase transitions on fixed connected graphs and random graphs in the presence of noise

Jialing Liu, Vikas Yadav, Huilas Sehgal, Joshua Olson, Haifeng Liu, Nicola Elia

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Scopus citations

Abstract

In this paper, we study phase transition behavior emerging from the interactions between multiple agents in the presence of noise. We propose a simple discrete-time model in which a group of non-mobile agents form either a fixed connected graph or a random graph process, and each agent, taking bipolar value either +1 or -1, updates its value according to its previous value and the noisy measurements of the connected agents' values. We present proofs for the occurrence of the following phase transition behavior: At a noise level higher than some threshold, the system generates symmetric behavior; whereas at a noise level lower than the threshold, the system exhibits spontaneous symmetry breaking. We also verify the phase transition using simulations. This result may be found useful in the study of the collective behavior of complex systems under communication constraints.

Original languageEnglish (US)
Title of host publicationProceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Pages734-739
Number of pages6
DOIs
StatePublished - Dec 1 2005
Externally publishedYes
Event44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 - Seville, Spain
Duration: Dec 12 2005Dec 15 2005

Publication series

NameProceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Volume2005

Other

Other44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
CountrySpain
CitySeville
Period12/12/0512/15/05

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  • Cite this

    Liu, J., Yadav, V., Sehgal, H., Olson, J., Liu, H., & Elia, N. (2005). Phase transitions on fixed connected graphs and random graphs in the presence of noise. In Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 (pp. 734-739). [1582244] (Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05; Vol. 2005). https://doi.org/10.1109/CDC.2005.1582244