Prof. Emo Welzl and Prof. Bernd Gärtner
|Mittagsseminar Talk Information|
Date and Time: Tuesday, May 14, 2013, 12:15 pm
Duration: 30 minutes
Location: CAB G51
Speaker: Hafsteinn Einarsson
Bootstrap percolation is a process of spread of activation/infections/rumours/defaults on a graph G. For a given initial active set the process proceeds in rounds where in each round we add to the set of active vertices all inactive vertices which have at least k active neighbours for some constant k. If, after the process terminates, the whole graph is active, we say that the initial set percolates.
The task of determining a sharp threshold for bootstrap percolation on the grid has been a popular topic since 1979 when it was first introduced by Chalupa, Leath and Reach. It was however not resolved completely until in 2012 by Balog, Bollobás, Duminil-Copin and Morris. I will talk about this result as well as a recent result by Janson, Luczak, Turova and Vallier who completely characterized Bootstrap Percolation on the Erdős–Rényi random graph.
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