  The voter model has been extensive studied as an opinion dynamic model, and
the role of the zealots has only been discussed recently. We introduce the
adaptive voter model with zealots and show that the final distribution of the
magnetism can be separated into two regions depending on the number of zealots
as well as the probability of forming link. When the fraction of zealots is
dominated in the population, the probability distribution of magnetism follows
a Gaussian-like distribution and the relaxation time is population-size
independent. When the population is dominated by the susceptible agents, the
relaxation time is proportional to the exponential of the population size. We
have found the analytical solution of the relaxation time in the limiting cases
and explained the difference of the relaxation time in these two regions based
on the approximation method.
