Berlin 2012 – scientific programme

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SOE: Fachverband Physik sozio-ökonomischer Systeme

SOE 22: Networks, From Topology to Dynamics IV (joint w. DY)

SOE 22.7: Talk

Friday, March 30, 2012, 11:30–11:45, MA 001

Continuous Percolation by Discontinuities — •Jan Nagler — MPI DS, Göttingen

The extent to which a complex network is connected crucially impacts its dynamics and function. Percolation, the transition to extensive connectedness on gradual addition of links, is often used to describe and model many different types of structure in the real world. How single links may explosively change macroscopic connectivity in networks where links add competitively according to certain rules has been debated extensively in the past three years. In the very recent article [Science 333, 322 (2011)], O. Riordan and L. Warnke state that (i) any rule based on picking a fixed number of random vertices gives a continuous transition, and (ii) that explosive percolation is continuous. It is equally true that certain percolation processes based on picking a fixed number of random vertices are discontinuous. Here we resolve this apparent paradox. We identify and analyze this by studying an extremal case of a process that is continuous in the sense of Riordan and Warnke but still exhibits infinitely many discontinuous jumps in an arbitrary vicinity of the transition point. We demonstrate analytically that continuity at the transition and discontinuity of the percolation process are compatible for certain competitive percolation systems.