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

Date and Time: Thursday, June 18, 2015, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Felix Weissenberger

Bootstrap Percolation with Inhibition: the Role of Edge Delays

We study bootstrap percolation on a random graph where each vertex is either excitatory or inhibitory and the information of having an active neighbour needs a certain time (delay) to be delivered: initially a subset of the vertices is activated; thereafter, a vertex gets active when it knows that it has k more excitatory than inhibitory active neighbours and stays active forever.

It is known that for deterministic delays of length 1 the size of the final active set is unstable in the size of the starting set (instability) and that exponentially distributed delays lead to a final active set whose size is independent of the size of the starting set (normalization).

We discuss the behaviour for more general delay distributions and show that the above cases are generic, i.e., all “tame” delay distributions lead to one of the two behaviours, either to instability or to normalization.

Joint work with Johannes Lengler and Angelika Steger

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