Heavy-tailed targets and (ab)normal asymptotics in diffusive motion

► We investigate the diffusive stochastic processes in the external potentials (EPs). ► Their probability densities (PDs) are described by the Fokker-Planck equation (FPE). ► Under suitable choice of EPs, the FPE generates heavy-tailed, rather than Gaussian PDs. ► We analyze the time dependence of the above probability density function variances.