  We study the heterogeneous dynamics of attractive colloidal particles close
to the gel transition using confocal microscopy experiments combined with a
theoretical statistical analysis. We focus on single particle dynamics and show
that the self part of the van Hove distribution function is not the Gaussian
expected for a Fickian process, but that it reflects instead the existence, at
any given time, of colloids with widely different mobilities. Our confocal
microscopy measurements can be described well by a simple analytical model
based on a conventional continuous time random walk picture, as already found
in several other glassy materials. In particular, the theory successfully
accounts for the presence of broad tails in the van Hove distributions that
exhibit exponential, rather than Gaussian, decay at large distance.
