Tagged particle diffusion in kinetically constrained models of glassy systems was analyzed. A method was presented, using the Kob-Andersen model as an example, which permitted the placing of lower and upper bounds on the self-diffusion coefficient, Ds. This method led to the exact density dependence of Ds, at high density, for models with finite defects and proved that Ds > 0, at any finite density, for highly cooperative models. A more general result was that, under very general assumptions, it was possible to exclude the possibility that a dynamic transition - like that predicted by the mode-coupling theory of glasses - took place at a finite temperature and chemical potential for systems of interacting particle on a lattice.

Dynamical Arrest, Tracer Diffusion and Kinetically Constrained Lattice Gases. C.Toninelli, G.Biroli: Journal of Statistical Physics, 2004, 117[1-2], 27-54