DOAJ Open Access 2003

Rigorous Result for the CHKNS Random Graph Model

Rick Durrett

Lihat Sumber DOI

Abstrak

We study the phase transition in a random graph in which vertices and edges are added at constant rates. Two recent papers in Physical Review E by Callaway, Hopcroft, Kleinberg, Newman, and Strogatz, and Dorogovstev, Mendes, and Samukhin have computed the critical value of this model, shown that the fraction of vertices in finite clusters is infinitely differentiable at the critical value, and that in the subcritical phase the cluster size distribution has a polynomial decay rate with a continuously varying power. Here we sketch rigorous proofs for the first and third results and a new estimates about connectivity probabilities at the critical value.

Topik & Kata Kunci

Mathematics

Penulis (1)

Rick Durrett

Format Sitasi

APA MLA BibTeX

Durrett, R. (2003). Rigorous Result for the CHKNS Random Graph Model. https://doi.org/10.46298/dmtcs.3345

Akses Cepat

Lihat di Sumber doi.org/10.46298/dmtcs.3345

Informasi Jurnal

Tahun Terbit: 2003
Sumber Database: DOAJ
DOI: 10.46298/dmtcs.3345
Akses: Open Access ✓