  We investigate the second spectrum of charge carrier density fluctuations in
graphene within the McWorther model, where noise is induced by electron traps
in the substrate. Within this simple picture, we obtain a closed-form
expression including both Gaussian and non-Gaussian fluctuations. We show that
a very extended distribution of switching rates of the electron traps in the
substrate leads to a carrier density power spectrum with a non-trivial
structure on the scale of the measurement bandwidth. This explains the
appearance of a $1/f$ component in the Gaussian part of the second spectrum,
which adds up to the expected frequency-independent term. Finally, we find that
the non-Gaussian part of the second spectrum can become quantitatively relevant
by approaching extremely low temperatures.
