Three-Dimensional Systems

In this chapter, we introduce the problem of concentric spheres in different dimensions and its main consequences related to mean first-passage times and splitting probabilities. For example, when the outer sphere goes to infinity, the splitting probability related to this boundary tends to zero for one and two dimensions, while being finite for systems with three dimensions or more. We also study the absorption of a disk over a flat reflecting wall. At steady state, we can find the rate constant for such a system. An important extension to any shape is given by the Dudko-Berezhkovskii-Weiss formula.