Fig. 8.

The ratio of the heterogeneous mean exit time ${\mathfrak{E}}_{n_0}$ to the homogeneous mean exit time ${ℰ}_{n_0}$ for randomly distributed barriers and antibarriers. We use a homogeneous propagator with a domain of size N = (51, 51) with absorbing boundary conditions, an initial condition at the center of the domain n₀ = (26, 26) and a diffusion parameter of q = (0.8, 0.8). The explicit form of ${\tilde{\phi }}_{n_0}(\mathit{n},z)$ is given by the z transform of Eq. (23) of Ref. [68]. Each curve is obtained using Eq. (10) and performing an ensemble average with 10² sample realizations of locations of barriers (λ > 0) or antibarriers (λ > 0) for each λ.