Thermalization of Lévy Flights: Path-Wise Picture in 2D

Figure 1

Gaussian target; statistics of 100000 random paths: surrogate pdf evolution and its OXY projection, displayed in the vertical order for 𝑡=0.2, 𝑡=0.7, and 𝑡=15. The bottom subfigure refer to the asymptotic pdf (14). All trajectories were started form the origin (0,0).

(a)

(b)

(c)

(d)