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.
| Original language | English |
|---|---|
| Pages (from-to) | 455-461 |
| Number of pages | 7 |
| Journal | Nature Physics |
| Volume | 16 |
| Issue number | 4 |
| DOIs | |
| State | Published - 1 Apr 2020 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2020, The Author(s), under exclusive licence to Springer Nature Limited.
Funding
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.
| Funders |
|---|
| Alexander von Humboldt-Stiftung |
| University of Tehran |
| Bundesministerium für Umwelt, Naturschutz, Bau und Reaktorsicherheit |