A new route to Explosive Percolation

The biased link occupation rule in the Achlioptas process (AP) discourages the large clusters from growing much ahead of others and encourages faster growth of clusters which lag behind. In this paper we propose a model where this tendency is sharply reflected in the Gamma distribution of the cluste...

Full description

Saved in:
Bibliographic Details
Published in:Physica A 2011-01, Vol.390 (2), p.177-182
Main Authors: Manna, S.S., Chatterjee, Arnab
Format: Article
Language:English
Subjects:
Clusters
Explosions
Explosive Percolation
First order transition
Graphs
Lattices
Mathematical models
Occupation
Percolation
Percolation phenomena
Statistical mechanics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The biased link occupation rule in the Achlioptas process (AP) discourages the large clusters from growing much ahead of others and encourages faster growth of clusters which lag behind. In this paper we propose a model where this tendency is sharply reflected in the Gamma distribution of the cluster sizes, unlike the power law distribution in AP. In this model single edges between pairs of clusters of sizes s i and s j are occupied with a probability ∝ ( s i s j ) α . The parameter α is continuously tunable over the entire real axis. Numerical studies indicate that for α < α c the transition is first order, α c = 0 for a square lattice and α c = − 1 / 2 for random graphs. In the limits of α = − ∞ , + ∞ this model coincides with models well established in the literature. ► A new route to Explosive Percolation has been defined and studied. ► This model gives a first order transition for a wide range of parameter values. ► The limiting cases of this model coincide with many well known models existing in the literature.
ISSN:0378-4371
1873-2119
DOI:10.1016/j.physa.2010.10.009