Continuous Percolation with Discontinuities

2012 | journal article. A publication with affiliation to the University of Göttingen.

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​Continuous Percolation with Discontinuities​
Nagler, J.; Tiessen, T. & Gutch, H. W.​ (2012) 
Physical Review X2(3) art. 031009​.​ DOI: https://doi.org/10.1103/PhysRevX.2.031009 

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Authors
Nagler, Jan; Tiessen, Tyge; Gutch, Harold W.
Abstract
Complex networks are a highly useful tool for modeling a vast number of different real world structures. Percolation describes the transition to extensive connectedness upon the gradual addition of links. Whether single links may explosively change macroscopic connectivity in networks where, according to certain rules, links are added competitively has been debated intensely in the past three years. In a recent article [O. Riordan and L. Warnke, Explosive Percolation is Continuous, Science 333, 322 ( 2011).], O. Riordan and L. Warnke conclude that (i) any rule based on picking a fixed number of random vertices gives a continuous transition, and (ii) that explosive percolation is continuous. In contrast, we show that it is equally true that certain percolation processes based on picking a fixed number of random vertices are discontinuous, and we resolve this apparent paradox. We identify and analyze a process that is continuous in the sense defined by Riordan and Warnke but still exhibits infinitely many discontinuous jumps in an arbitrary vicinity of the transition point: a Devil's staircase. We demonstrate analytically that continuity at the first connectivity transition and discontinuity of the percolation process are compatible for certain competitive percolation systems.
Issue Date
2012
Status
published
Publisher
Amer Physical Soc
Journal
Physical Review X 
Organization
Fakultät für Physik 
ISSN
2160-3308

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