  We investigate the time evolution of higher order cumulants of conserved
charges in a volume with the diffusion master equation. Applying the result to
the diffusion of non-Gaussian fluctuations in the hadronic stage of
relativistic heavy ion collisions, we show that the fourth-order cumulant of
net-electric charge at LHC energy is suppressed compared with the recently
observed second-order cumulant at ALICE, if the higher order cumulants at
hadronization are suppressed compared with their values in the hadron phase in
equilibrium. The significance of the experimental information on the rapidity
window dependence of various cumulants in investigating the history of the
dynamical evolution of the hot medium created in relativistic heavy ion
collisions is emphasized.
