Higher order corrections for anisotropic bootstrap percolation

Bootstrap percolation is a very simple model for growth from a random initial configuration on finite lattices. The model has many applications, for instance to model the spread of infections and to model magnets at low temperatures, to name two, but it is also interesting from a purely mathematical perspective. The model parameter has a critical value, at which the behaviour changes sharply. One interesting feature of bootstrap percolaton is a phenomenon called the “bootstrap paradox” which relates to a big discrepancy between numerical and theoretical estimates of the critical value of bootstrap percolation models.
I will discuss work in progress in which we give the most accurate theoretical estimate for the critical value of any bootstrap model to date, compare it with new numerical estimates, and show how it (tentatively) resolves the paradox.
This talk is based on joint work with Hugo Duminil-Copin, Aernout van Enter, and Rob Morris, and on work with Robert Fitzner.