Watersheds and Explosive percolation
arXiv:1103.0765 · doi:10.1016/j.phpro.2011.05.057
Abstract
The recent work by Achlioptas, D'Souza, and Spencer opened up the possibility of obtaining a discontinuous (explosive) percolation transition by changing the stochastic rule of bond occupation. Despite the active research on this subject, several questions still remain open about the leading mechanism and the properties of the system. We review the largest cluster and the Gaussian models recently introduced. We show that, to obtain a discontinuous transition it is solely necessary to control the size of the largest cluster, suppressing the growth of a cluster differing significantly, in size, from the average one. As expected for a discontinuous transition, a Gaussian cluster-size distribution and compact clusters are obtained. The surface of the clusters is fractal, with the same fractal dimension of the watershed line.
to appear in the Proceedings of the 24th Annual CSP Workshop
References in corpus (22)
- Universality classes in nonequilibrium lattice systems
- "Explosive Percolation" Transition is Actually Continuous
- Self-organized adaptation of a simple neural circuit enables complex robot behaviour
- Impact of Single Links in Competitive Percolation -- How complex networks grow under competition
- Explosive percolation in scale-free networks
- Explosive percolation via control of the largest cluster
- Percolation Transitions in Scale-Free Networks under Achlioptas Process
- Construction and Analysis of Random Networks with Explosive Percolation
- Explosive percolation: a numerical analysis
- Local cluster aggregation models of explosive percolation
- Strongly discontinuous explosive percolation with multiple giant components
- Scaling behavior of explosive percolation on the square lattice
- Cluster aggregation model for discontinuous percolation transition
- Tricritical point in explosive percolation
- A new route to Explosive Percolation
- Fracturing the optimal paths
- Explosive Percolation in the Human Protein Homology Network
- A Hamiltonian approach for explosive percolation
- Optimal path cracks in correlated and uncorrelated lattices
- Transport on exploding percolation clusters
- Impact of Perturbations on Watersheds
- Criterion for explosive percolation transitions on complex networks