Fig. 7.

Time-dependent first-passage probability to either of two targets in the presence of heterogeneities. The location of the targets n₁ = (4, 2) and n₂ = (10, 7) in relation to the initial condition n₀ = (6, 6) and visualization of the heterogeneities present can be seen in the schematic diagram in Fig. 1. We use a homogeneous propagator ${\tilde{\phi }}_{n_0}(\mathit{n},z)$ with a reflecting domain of size N = (10, 10) and a diffusion parameter of value q = (0.2, 0.2). The explicit form of ${\tilde{\phi }}_{n_0}(\mathit{n},z)$ is given by Eq. (23) of Ref. [68]. The lines are obtained through numerical inversion of the generating function of the first-passage probability to either of two targets (see text), while the corresponding marks—shown only in panel (a)—are obtained through 1.5 × 10⁶ stochastic simulations.