Figure 1
Illustration: Alan Stonebraker

Figure 1: In continuous-time random walks, the walker’s position is governed only by the number of preceding steps. This number of steps n(t) constitutes the operational time of the problem as recorded by the walker’s own clock, which ticks once each time n is incremented. Since n(t) grows slower than linearly with the physical (clock) time, this watch is always behind, leading to the overall subdiffusive behavior, as compared with the otherwise normal random walk. He et al. have used this model to study time-averaged single-molecule behavior in comparison with ensemble averages of many molecules.