Bootstrap Percolation and Partial Difference Equations

Nikolai Beluhov studies a bootstrap-percolation process on the integer lattice in which each new occupied point completes one of a fixed set of patterns. The problem is to determine the smallest seed that eventually percolates. For two patterns in two dimensions, the answer is essentially determined by the mixed volume of their convex hulls. Motivated by partial difference equations, the analysis also yields a consistency criterion for systems of two such equations in two dimensions.