Interevent time distribution, burst, and hybrid percolation transition
Abstract
Critical phenomena of a second-order percolation transition are known to be independent of cluster merging or pruning process. However, those of a hybrid percolation transition (HPT), mixed properties of both first-order and second-order transitions, depend on the processes. The HPT induced by cluster merging is more intrigue and little understood than the other. Here, we construct a theoretical framework using the so-called restricted percolation model. In this model, clusters are ranked by size and partitioned into small- and large-cluster sets. As the cluster rankings are updated by cluster coalescence, clusters may move back and forth across the set boundary. The inter-event time (IET) between two consecutive crossing times have two distributions with power-law decays, which in turn characterize the criticality of the HPT. A burst of such crossing events occurs and signals the upcoming transition. We discuss a related phenomenon to this critical dynamics.
Keywords
Cite
@article{arxiv.1906.03484,
title = {Interevent time distribution, burst, and hybrid percolation transition},
author = {Jinha Park and Sudo Yi and K. Choi and Deokjae Lee and B. Kahng},
journal= {arXiv preprint arXiv:1906.03484},
year = {2020}
}