  We discuss the effect of external noisy magnetic fields on mesoscopic spin
fluctuations that can be probed in semiconductors and atomic vapors by means of
optical spin noise spectroscopy (SNS). We show that conventional arguments of
the law of large numbers do not apply to spin correlations induced by external
fields, namely, the magnitude of the 4th order spin cumulant grows as $\sim
N^2$ with the number $N$ of observed spins, i.e. it is not suppressed in
comparison to the 2nd order cumulant. This allows us to design a simple
experiment to measure the 4th order cumulant of spin fluctuations in an atomic
system near thermodynamic equilibrium and develop quantitative theory that
explains all observations.
