  Jamming, or dynamical arrest, is a transition at which many particles stop
moving in a collective manner. In nature it is brought about by, for example,
increasing the packing density, changing the interactions between particles, or
otherwise restricting the local motion of the elements of the system. The onset
of collectivity occurs because, when one particle is blocked, it may lead to
the blocking of a neighbor. That particle may then block one of its neighbors,
these effects propagating across some typical domain of size named the
dynamical correlation length. When this length diverges, the system becomes
immobile. Even where it is finite but large the dynamics is dramatically
slowed. Such phenomena lead to glasses, gels, and other very long-lived
nonequilibrium solids. The bootstrap percolation models are the simplest
examples describing these spatio-temporal correlations. We have been able to
solve one such model in two dimensions exactly, exhibiting the precise
evolution of the jamming correlations on approach to arrest. We believe that
the nature of these correlations and the method we devise to solve the problem
are quite general. Both should be of considerable help in further developing
this field.
