When each particle in the anomalous file is assigned with its own jumping time drawn form ψ ψ α α ( t ) ( ψ ψ α α ( t ) is the same for all the particles), the anomalous file is not a renewal file. The basic dynamical cycle in such a file consists of the following steps: a particle with the fastest jumping time in the file, say, t i for particle i, attempts a jump. Then, the waiting times for all the other particles are adjusted: we subtract t i from each of them. Finally, a new waiting time is drawn for particle i. The most crucial difference among renewal anomalous files and anomalous files that are not renewal is that when each particle has its own clock, the particles are in fact connected also in the time domain, and the outcome is further slowness in the system (proved in the main text). The equation of motion for the PDF in anomalous files of independent particles reads: