  We study consequences of long-range elasticity in thermally assisted dynamics
of yield stress materials. Within a two-dimensinal mesoscopic model we
calculate the mean-square displacement and the dynamical structure factor for
tracer particle trajectories. The ballistic regime at short time scales is
associated with a compressed exponential decay in the dynamical structure
factor, followed by a subdiffusive crossover prior to the onset of diffusion.
We relate this crossover to spatiotemporal correlations and thus go beyond
established mean field predictions.
