# Mathematics Colloquia and Seminars

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### Protection of an unstable equilibrium by inert obstacles

**PDE and Applied Math Seminar**

Speaker: | Prof. Janko Gravner, UC Davis |

Location: | 2112 MSB |

Start time: | Wed, Dec 31 1969, 4:10PM |

Bootstrap percolation is a simple mechanism by which an unstable equilibrium may be replaced by a stable one. Consider a uniform configuration of empty sites on the d-dimensional integer lattice, add a random smattering of occupied sites, and then iteratively occupy all sites with at least threshold theta occupied neighbors. A classic result of van Enter and Schonmann is that, provided theta is no larger than d and the initial density of occupied sites is positive, every site is eventually occupied.

What if a small proportion of sites is forever prevented from becoming occupied?

We will describe recent progress on this problem, which is joint work with A. Holroyd

and D. Sivakoff.