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University of Cambridge > Talks.cam > Combinatorics Seminar > Bootstrap Percolation in the Hypercube

## Bootstrap Percolation in the HypercubeAdd to your list(s) Download to your calendar using vCal - Natasha Morrison (Oxford)
- Thursday 22 October 2015, 14:30-15:30
- MR12.
If you have a question about this talk, please contact Andrew Thomason. The \emph{$r$-neighbour bootstrap process} on a graph $G$ starts with an initial set of ``infected’’ vertices and, at each step of the process, a healthy vertex becomes infected if it has at least $r$ infected neighbours (once a vertex becomes infected, it remains infected forever). If every vertex of $G$ becomes infected during the process, then we say that the initial set \emph{percolates}. In this talk I will discuss the proof of a conjecture of Balogh and Bollob\’{a}s: for fixed $r$ and $d\to\infty$, the minimum cardinality of a percolating set in the $d$-dimensional hypercube is $\frac{1+o(1)}{r}\binom{d}{r-1}$. One of the key ideas behind the proof exploits a connection between bootstrap percolation and weak saturation. This is joint work with Jonathan Noel. This talk is part of the Combinatorics Seminar series. ## This talk is included in these lists:- All CMS events
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