Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Thursday, June 29, 2017, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Christoph Koch (University of Warwick)

How to (re-)establish a brand: bootstrap percolation in social networks

We consider a classical and well-studied graph process called bootstrap percolation. While bootstrap percolation originally arose in the context of disordered magnetic systems, it has become an important model in the description and analysis of dynamics in social networks. Initially some vertices in a graph are activated, and subsequently each vertex with at least r>1 active neighbours is activated as well. Once a vertex is active, it remains so forever. On a variety of random graph models it is known that even (reasonably) sparse initial activations are likely to cause an activation of most vertices in the graph. However, for other models this critical phenomenon does not occur. We investigate this dichotomy in detail and determine almost tight criteria on the degree sequence of random graphs for both the existence and non-existence of this critical phenomenon. These results are joint work with N. Fountoulakis (Birmingham), M. Kang (TU Graz), and T. Makai (TU Graz).

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