Random walks time resolution

We assume that the time resolution of the STM-measurements is sufficient to discriminate the effect of the entire random walk of one individual vacancy from that of the next, which was already shown to be the case in Section 2.2. The starting situation is shown in Fig. 13. A tracer atom is embedded in the origin of a square lattice with a vacancy sitting next to it at (1, 0). We assume that the only diffusion barrier that is modified by the tracer atom is that for vacancy-tracer exchange. 

Brownian motion, also referred to as a random walk or Wiener process, is named after the Scottish botanist Robert Brown, who in 1828 [22] described the erratic motion of pollen in aqueous suspensions observed with a light microscope. A particle undergoing Brownian motion seems to wander around without any distinct pattern (Figure 2.9). Some regions of the plane are filled densely by the particle s trace. Increasing the resolution of the microscope and the time resolution produces a random walk that looks very much like that obtained at lower resolution. 

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