Random Interactions
A new route to Explosive Percolation
by Dr. Subhrangshu Sekhar Manna (S.N. Bose National Centre for Basic Sciences, Kolkata)
Monday, April 11, 2011
from
to
(Asia/Kolkata)
at Colaba Campus ( A-304 )
at Colaba Campus ( A-304 )
Description |
The biased link occupation rule in the Achlioptas process (AP) discourages the large clusters to grow 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 $\propto (s_is_j)^{\alpha}$. The parameter $\alpha$ is continuously tunable over the entire real axis. Numerical studies indicate that for $\alpha < \alpha_c$ the transition is first order, $\alpha_c=0$ for square lattice and $\alpha_c=-1/2$ for random graphs. In the limits of $\alpha = -\infty, +\infty$ this model coincides with models well established in the literature. |
Organised by | Dr. Vikram Tripathi |