Abstract
We study various models of independent particles hopping between energy `traps' with a density of energy barriers 
, on a d-dimensional lattice or on a fully connected lattice. If decays exponentially, a true dynamical phase transition between a high-temperature `liquid' phase and a low-temperature `aging' phase occurs. More generally, however, one expects that for a large class of , `interrupted' aging effects appear at low enough temperatures, with an ergodic time growing faster than exponentially. The relaxation functions exhibit a characteristic shoulder, which can be fitted as stretched exponentials. A simple way of introducing interactions between the particles leads to a modified model with an effective diffusion constant in energy space, which we discuss in detail.