Dresden 2020 – wissenschaftliches Programm
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DY 1: Tutorials: Stochastic Processes from Financial Risk to Dynamics in Biology and Physics (joint session SOE/TUT/DY)
DY 1.2: Tutorium
Sonntag, 15. März 2020, 16:50–17:40, HSZ 03
From Percolation and Explosive Percolation to a unifying principle — •Jan Nagler — Frankfurt School of F&M, Frankfurt, Germany
The emergence of large-scale connectivity crucially underlies the structure, proper functioning, and failure of many complex socio-technical networks. For many decades, percolation was studied predominately as a second-order phase transition where at the critical threshold, the order parameter increases in a rapid but continuous way. In 2009, an explosive, i.e. extremely rapid, transition was found for a network growth process where links compete for addition. This observation of "explosive percolation" started an enormous surge of analyzing explosive phenomena and their consequences. Many models are now shown to yield discontinuous explosive percolation transitions, and some models exhibit a hybrid transition with a combination of second- and first- order features. Important mechanisms that achieve the required delay for explosive transitions include history dependence, non-self-averaging, and strong correlations. In this tutorial we will start to review standard percolation and end with "explosive phenomena" in networked systems. Examples include social systems, globalization, and the emergence of molecular life [D'Souza, Gomez-Gardenes, Nagler, Arenas, Explosive phenomena in complex networks, Advances in Physics 68(3):123, 2019]. We will close with some recent publication that provides a unifying framework for continuous, discontinuous and even hybrid phase transitions [Fan, Meng, Liu, Saberi, Kurths, Nagler, Universal gap scaling in percolation, Nature Physics, in press].