  We consider the effects of a noisy magnetic field background over the fermion
propagator in QED, as an approximation to the spatial inhomogeneities that
would naturally arise in certain physical scenarios, such as heavy-ion
collisions or the quark-gluon plasma in the early stages of the evolution of
the Universe. We considered a classical, finite and uniform average magnetic
field background $\langle\mathbf{B}(\mathbf{x})\rangle = \mathbf{B}$, subject
to white-noise spatial fluctuations with auto-correlation of magnitude
$\Delta_B$. By means of the Schwinger representation of the propagator in the
average magnetic field as a reference system, we used the replica formalism to
study the effects of the magnetic noise in the form of renormalized
quasi-particle parameters, leading to an effective charge and an effective
refraction index, that depend not only on the energy scale, as usual, but also
on the magnitude of the noise $\Delta_B$ and the average field $\mathbf{B}$.
