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

Date and Time: Tuesday, May 14, 2013, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Hafsteinn Einarsson

A short survey on bootstrap percolation

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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