# Noon lecture

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On 24.09.2015 at 12:20 in S6, there is the following noon lecture:

# Extremal Bounds for Bootstrap Percolation in the Hypercube

## Jonathan Noel

## Abstract

The r-neighbour bootstrap process on a graph G begins with an initial set of "infected" vertices and, at each step of the process, a previously healthy vertex becomes infected if it has at least r infected neighbours. The set of initially infected vertices is said to percolate if the infection spreads to the entire vertex set.

In this talk, we will present a proof of a conjecture of Balogh and Bollobás which says that the minimum size of a percolating set for the r-neighbour bootstrap process in the d-dimensional hypercube is asymptotically (1/r) (d choose r-1). We will also place this result in context by discussing some of the major results in bootstrap percolation. This is joint work with Natasha Morrison.

list of noon lectures ( 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | future lectures)

Webmaster: kamweb.mff.cuni.cz Modified: 19. 10. 2010