Por Byungnam Kahng (Department of Physics and Astronomy, Seoul National University).
Abstract: Recently, hybrid percolation transitions (HPTs) have received considerable attention from the scientific community. They exhibit properties of both first-order and second-order percolation transitions at the same transition point. HPTs may be classified into two types: those induced I) by cascading dynamics and II) by cluster merging dynamics. Type-I HPTs, for instance, arising in k-core percolation and contagion model, have been extensively studied. The critical branching process arising in the Bak–Tang–Wiesenfeld (BTW) type of self-organized criticality (SOC) behavior, acts as the underlying mechanism and characterizes the critical behavior of the type-I HPT. However, type-II HPTs have not yet been widely studied, because the problem was somewhat intrigue; however, its role in statistical physics and network science is regarded important. Theory for the type II HPT is not established yet. In this presentation, I will report our recent progress for the investigation of underlying mechanism on a microscopic level and the construction of a theoretical framework for the type-II HPT. We found that a new type of SOC phenomenon underlies it. This SOC behavior is distinct from the conventional BTW-type SOC avalanche dynamics, and has never been reported in statistical physics literature in association with percolation transitions, to the best of my knowledge. We established a theoretical framework, within the existing framework of percolation theory, even though details are very different.