Phase transitions for modified Erdős–Rényi processes

Svante Janson Department of Mathematics, Uppsala University Joel Spencer Courant Institute, New York University

Optimization and Control Probability mathscidoc:1701.27004

Arkiv for Matematik, 50, (2), 305-329, 2010.5
A fundamental and very well studied region of the Erdős–Rényi process is the phase transition at$m$∼$n$/2 edges in which a giant component suddenly appears. We examine the process beginning with an initial graph. We further examine the Bohman–Frieze process in which edges between isolated vertices are more likely. While the positions of the phase transitions vary, the three processes belong, roughly speaking, to the same universality class. In particular, the growth of the giant component in the barely supercritical region is linear in all cases.
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  title={Phase transitions for modified Erdős–Rényi processes},
  author={Svante Janson, and Joel Spencer},
  booktitle={Arkiv for Matematik},
Svante Janson, and Joel Spencer. Phase transitions for modified Erdős–Rényi processes. 2010. Vol. 50. In Arkiv for Matematik. pp.305-329.
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