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Journal Article

Universal gap scaling in percolation


Fan,  Jingfang
Potsdam Institute for Climate Impact Research;


Meng,  Jun
Potsdam Institute for Climate Impact Research;


Liu,  Yang
Potsdam Institute for Climate Impact Research;

Ali Saberi,  A.
External Organizations;


Kurths,  Jürgen
Potsdam Institute for Climate Impact Research;

Nagler,  J.
External Organizations;

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Fan, J., Meng, J., Liu, Y., Ali Saberi, A., Kurths, J., Nagler, J. (2020): Universal gap scaling in percolation. - Nature Physics, 16, 4, 455-461.

Cite as: https://publications.pik-potsdam.de/pubman/item/item_23575
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.