26.04.2018 | 12:15 bis 13:00

Bernoullis Tafelrunde: Thomas Hayder

Percolation on the Erdös-Renyi model

Given a random graph, how does the structure of the connected components look like? This is the central question in percolation theory. One of the most important structure properties of this random graphs is the size of the largest connected component.

After a short introduction of some random graph models and its applications in various sciences, i will focus on the Erdös-Renyi model. I will introduce the branching process, and give a short overview, how this process can be used to explore the connected components in the Erdös-Renyi model. As a result, we will see that the size of the largest connected component undergoes a phase transition.

Keywords: Percolation, random graph, Erdös-Renyi model, branching process, phase transition