  The hydrogen dynamics on a graphene sheet is studied in the presence of
carbon vacancies. We analyze the motion of atomic H by means of molecular
dynamics (MD) simulations, using a tight-binding Hamiltonian fitted to
density-functional calculations. Hydrogen passivates the dangling bonds of C
atoms close to a vacancy, forming C--H bonds with H located at one or the other
side of the layer plane. The hydrogen dynamics has been studied from
statistical analysis of MD trajectories, along with the autocorrelation
function of the atomic coordinates. For a single H atom, we find an effective
barrier of 0.40~eV for crossing the graphene layer, with a jump rate $\nu = 2
\times 10^6$~s$^{-1}$ at 300~K. The atomic jumps behave as stochastic events,
and their number for a given temperature and time interval follows a Poisson
probability distribution. For two H atoms close to a vacancy, strong
correlations in the atomic dynamics are found, with a lower jump frequency $\nu
= 7 \times 10^2$~s$^{-1}$ at room temperature. These results provide insight
into the diffusion mechanisms of hydrogen on graphene, paving the way for a
complete understanding of its motion through defective crystalline membranes.
