Extreme Fluctuations in Small-Worlds with Relaxational Dynamics

Details Extreme Fluctuations in Small-Worlds with Relaxational Dynamics Extreme Fluctuations in Small-Worlds with Relaxational Dynamics

2003-11-25

arxiv.org/abs/cond-mat/0311575v1

Phys. Rev. E 69, 065104(R) (2004).

Physics

Condensed Matter

Statistical Mechanics

4 pages, 2 figures

Scientific paper

10.1103/PhysRevE.69.065104

We study the distribution and scaling of the extreme height fluctuations for Edwards-Wilkinson-type relaxation on small-world substrates. When random links are added to a one-dimensional lattice, the average size of the fluctuations becomes finite (synchronized state) and the extreme height diverges only logarithmically in the large system-size limit. This latter property ensures synchronization in a practical sense in small-world coupled multi-component autonomous systems. The statistics of the extreme heights is governed by the Fisher-Tippett-Gumbel distribution.

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