  We calculate the fluctuations in the current and energy densities for the
case of a quantized, minimally coupled, massless, complex scalar field around a
straight and infinitesimally thin cosmic string carrying magnetic flux. At zero
temperature, we evaluate the fluctuations in the current and energy densities
for arbitrary flux and deficit angle. At a finite temperature, we evaluate the
fluctuations in the energy density for the special case wherein the flux is
absent and the deficit angle equals $\pi$. We find that, quite generically, the
dimensionless ratio of the variance to the mean-squared values of the current
and energy densities are of order unity which suggests that the fluctuations
around cosmic strings can be considered to be large.
