  In this article, we consider the propagation of QED fermions in the presence
of a classical background magnetic field with white-noise stochastic
fluctuations. The effects of the magnetic field fluctuations are incorporated
into the fermion and photon propagators in a quasi-particle picture, which we
developed in previous works using the {\it replica trick}. By considering the
strong-field limit, here we explicitly calculate the fermion self-energy
involving radiative contributions at first-order in $\alpha_\text{em}$, in
order to obtain the noise-averaged mass of the fermion propagating in the
fluctuating magnetized medium. Our analytical results reveal a leading
double-logarithmic contribution $\sim \left[\ln \left( |e B|/m^2
\right)\right]^2$ to the mass, with an imaginary part representing a spectral
broadening proportional to the magnetic noise auto-correlation $\Delta$. While
a uniform magnetic field already breaks Lorentz invariance, inducing the usual
separation into two orthogonal subspaces (perpendicular and parallel with
respect to the field), the presence of magnetic noise further breaks the
remaining symmetry, thus leading to distinct spectral widths associated with
fermion and anti-fermion, and their spin projection in the quasi-particle
picture.
