  We study the behavior of classical dimer coverings of the square lattice - a
paradigmatic model for systems subject to constraints - evolving under local
stochastic dynamics, by means of Monte Carlo simulations and theoretical
arguments. We observe clear signatures of correlated dynamics in both global
and local observables and over a broad range of time scales, indicating a
breakdown of the simple continuum description that approximates well the
statics. We show that this collective dynamics can be understood in terms of
one-dimensional "strings" of high mobility, which govern both local and
long-wavelength dynamical properties. We introduce a coarse-grained description
of the strings, based on the Edwards-Wilkinson model, which leads to exact
results in the limit of low string density and provides a detailed qualitative
understanding of the dynamics in all flux sectors. We discuss the implications
of our results for the dynamics of constrained systems more generally.
