Name
Abstract | ||
|---|---|---|
We determine the asymptotic size of the largest component in the 2-type binomial random graph G(n, P) near criticality using a refined branching process approach. In G(n, P) every vertex has one of two types, the vector n describes the number of vertices of each type, and any edge {u, v} is present independently with a probability that is given by an entry of the probability matrix P according to the types of u and v. We prove that in the weakly supercritical regime, i.e., if the "distance" to the critical point of the phase transition is given by epsilon = epsilon(n) -> 0, with probability 1 - o(1), the largest component in G(n, P) contains asymptotically 2 epsilon parallel to n parallel to(1) vertices and all other components are of size o(epsilon parallel to n parallel to(1)). |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1137/140973256 | SIAM JOURNAL ON DISCRETE MATHEMATICS |
Keywords | DocType | Volume |
random graphs,phase transition,largest component,branching process | Journal | 29 |
Issue | ISSN | Citations |
2 | 0895-4801 | 0 |
PageRank | References | Authors |
0.34 | 0 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Mihyun Kang | 1 | 163 | 29.18 |
| Christoph Koch | 2 | 0 | 0.34 |
| Angélica Pachón | 3 | 0 | 0.34 |