Approaching stationarity : competition between long jumps and longwaiting times

Within the continuous-time random walk (CTRW) scenarios, properties of the overall motion are determined by the waiting time and the jump length distributions. In the decoupled case, with power-law distributed waiting times and jump lengths, the CTRW scenario is asymptotically described by the double (space and time) fractional Fokker–Planck equation. Properties of a system described by such an equation are determined by the subdiffusion parameter and the jump length exponent. Nevertheless, the stationary state is determined solely by the jump length distribution and the potential. The waiting time distribution determines only the rate of convergence to the stationary state. Here, we inspect the competition between long waiting times and long jumps and how this competition is reflected in the way in which a stationary state is reached. In particular, we show that the distance between a time-dependent and a stationary solution changes in time as a double power law