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Protection of an unstable equilibrium by inert obstacles

Mathematical Physics & Probability

Speaker: Prof. Janko Gravner, UC Davis
Location: 2112 MSB
Start time: Wed, Jan 16 2019, 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.