  We study the onset of the bootstrap percolation transition as a model of
generalized dynamical arrest. We develop a new importance-sampling procedure in
simulation, based on rare events around "holes", that enables us to access
bootstrap lengths beyond those previously studied. By framing a new theory in
terms of paths or processes that lead to emptying of the lattice we are able to
develop systematic corrections to the existing theory, and compare them to
simulations. Thereby, for the first time in the literature, it is possible to
obtain credible comparisons between theory and simulation in the accessible
density range.

Statistical Mechanics;Disordered Systems and Neural Networks