In renewal-anomalous files, a random period is taken independently from a waiting time probability density function (WT-PDF; see Continuous-time Markov process for more information) of the form: ψ ψ α α ( t ) ∼ ∼ k ( k t ) − − 1 − − α α , 0 < α α ≤ ≤ 1 , where k is a parameter. Then, all the particles in the file stand still for this random period, where afterwards, all the particles attempt jumping in accordance with the rules of the file. This procedure is carried on over and over again. The equation of motion for the particles’ PDF in a renewal-anomalous file is obtained when convoluting the equation of motion for a Brownian file with a kernel k α α ( t ) :