Abstract
Universality is a principle that fundamentally underlies many critical phenomena, ranging from epidemic spreading to the emergence or breakdown of global connectivity in networks. Percolation, the transition to global connectedness on gradual addition of links, may exhibit substantial gaps in the size of the largest connected network component. We uncover that the largest gap statistics is governed by extreme-value theory. This allows us to unify continuous and discontinuous percolation by virtue of universal critical scaling functions, obtained from normal and extreme-value statistics. Specifically, we show that the universal scaling function of the size of the largest gap is given by the extreme-value Gumbel distribution. This links extreme-value statistics to universality and criticality in percolation.
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Code availability
The C++ and Python codes used for the analysis is available on GitHub (https://github.com/fanjingfang/Universal-gap-scaling-in-percolation). All figures are plotted by Origin 2018.
Change history
24 February 2020
A Correction to this paper has been published: https://doi.org/10.1038/s41567-020-0837-5
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Acknowledgements
We acknowledge the ‘East Africa Peru India Climate Capacities — EPICC’ project, which is part of the International Climate Initiative (IKI). The Federal Ministry for the Environment, Nature Conservation and Nuclear Safety (BMU) supports this initiative on the basis of a decision adopted by the German Bundestag. The Potsdam Institute for Climate Impact Research (PIK) is leading the execution of the project together with its project partners The Energy and Resources Institute (TERI) and the Deutscher Wetterdienst (DWD). A.A.S. acknowledges support from the Alexander von Humboldt Foundation and partial financial support from the research council of the University of Tehran.
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J.F., J.M., A.A.S., J.K. and J.N. designed the research, conceived the study, carried out the analysis and prepared the manuscript. J.F., J.M. and J.N. analysed data. J.F., J.M., Y.L., A.A.S. and J.N. discussed results and contributed to writing the manuscript.
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Fan, J., Meng, J., Liu, Y. et al. Universal gap scaling in percolation. Nat. Phys. 16, 455–461 (2020). https://doi.org/10.1038/s41567-019-0783-2
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DOI: https://doi.org/10.1038/s41567-019-0783-2
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