Abstract (EN)

Consider a sequence of possibly random graphs GN=(VN,EN), N≥1, whose vertices's have i.i.d. weights {WNx:x∈VN} with a distribution belonging to the basin of attraction of an α-stable law, 0<α<1. Let XNt, t≥0, be a continuous time simple random walk on GN which waits a \emph{mean} WNx exponential time at each vertex x. Under considerably general hypotheses, we prove that in the ergodic time scale this trap model converges in an appropriate topology to a K-process. We apply this result to a class of graphs which includes the hypercube, the d-dimensional torus, d≥2, random d-regular graphs and the largest component of super-critical Erd\"os-R\'enyi random graphs.