Universal gap scaling in percolation

Jingfang Fan, Jun Meng, Yang Liu, Abbas Ali Saberi, Jürgen Kurths, Jan Nagler

Research output: Contribution to journalArticlepeer-review

29 Scopus citations


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.

Original languageEnglish
Pages (from-to)455-461
Number of pages7
JournalNature Physics
Issue number4
StatePublished - 1 Apr 2020
Externally publishedYes

ASJC Scopus subject areas

  • General Physics and Astronomy


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