Percolation in a hierarchical random graph

Details Percolation in a hierarchical random graph Percolation in a hierarchical random graph

2006-07-05

arxiv.org/abs/math/0607131v2

Mathematics

Probability

19 pages and 1 figure

Scientific paper

We study asymptotic percolation as $N\to \infty$ in an infinite random graph ${\cal G}_N$ embedded in the hierarchical group of order $N$, with connection probabilities depending on an ultrametric distance between vertices. ${\cal G}_N$ is structured as a cascade of finite random subgraphs of (approximate) Erd\"os-Renyi type. We give a criterion for percolation, and show that percolation takes place along giant components of giant components at the previous level in the cascade of subgraphs for all consecutive hierarchical distances. The proof involves a hierarchy of random graphs with vertices having an internal structure and random connection probabilities.

Affiliated with

Also associated with

No associations

Rating

Percolation in a hierarchical random graph does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Percolation in a hierarchical random graph, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Percolation in a hierarchical random graph will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-450763