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DY: Fachverband Dynamik und Statistische Physik

DY 29: Statistical physics of complex networks

DY 29.9: Talk

Friday, March 27, 2009, 12:30–12:45, ZEU 255

Deformed Gaussian Orthogonal Ensemble description of Small-World networks — •Josue Xavier de Carvalho¹, Sarika Jalan¹, and Mahir Saleh Hussein^1,2 — ¹MPIPKS, Dresden, Germany — ²USP, Sao Paulo, Brazil

The study of spectral behaviour of networks has gained enthusiasm over the last few years. In particular, Random Matrix Theory concepts have proven to be useful. In discussing transitions from regular behaviour to fully chaotic behaviour it has been found that an extrapolation formula of the Brody type can be used. In the present paper we analyse the regular to chaotic behaviour of Small World networks using an extention of Wigner’s Gaussian Orthogonal Ensemble. This RMT, coined the Deformed Gaussian Orthognal Ensemble, supplies a natural foundation of Brody’s formula. The analysis performed in this paper proves the utility of the DGOE in network physics, as much as it has been useful in other physical systems.