  The effective low-energy late-time description of many body systems near
thermal equilibrium provided by classical hydrodynamics in terms of dissipative
transport phenomena receives important corrections once the effects of
stochastic fluctuations are taken into account. One such physical effect is the
occurrence of long-time power law tails in correlation functions of conserved
currents. In the hydrodynamic regime $\vec{k} \rightarrow 0$ this amounts to
non-analytic dependence of the correlation functions on the frequency $\omega$.
In this article, we consider a relativistic fluid with a conserved global
$U(1)$ charge in the presence of a strong background magnetic field, and
compute the long-time tails in correlation functions of the stress tensor. The
presence of the magnetic field renders the system anisotropic. In the absence
of the magnetic field, there are three out-of-equilibrium transport parameters
that arise at the first order in the hydrodynamic derivative expansion, all of
which are dissipative. In the presence of a background magnetic field, there
are ten independent out-of-equilibrium transport parameters at the first order,
three of which are non-dissipative and the rest are dissipative. We provide the
most general linearized equations about a given state of thermal equilibrium
involving the various transport parameters in the presence of a magnetic field,
and use them to compute the long-time tails for the fluid.
