Figure 3.

(a) Probability distribution of the heavy particle at time t=1 computed by the multi-scale algorithm [M1]–[M8] (grey histogram) is compared with the distribution (4.9) given by the BD model (2.6) (black solid line). (b) The time evolution of the mean squared displacement computed by 10⁵ realizations of the algorithm [M1]–[M8] (solid line) is compared with equation (2.13) (dashed line) and $\sqrt{2Dt}$ (dot-dashed line). We use μ=10³, γ=10, D=1, Δt=10⁻⁷, L=10, R=1, X(0)=0 and V (0)=0. (Online version in colour.)