  We perform spin-noise spectroscopy on an unpolarized $^{87}\mathrm{Rb}$ vapor
in the spin-exchange-relaxation-free (SERF) regime. We observe noise spectral
distributions that deviate strongly from Lorentzian models that accurately
describe lower-density regimes. For example, at magnetic fields of $\sim 1
\mathrm{\mu T}$ and $^{87}\mathrm{Rb}$ densities $\gtrsim 1 \times 10^{14}
\rm{atoms/cm^{3}}$ we observe an asymmetric spin-noise distribution in which
the resonance line is depleted by about half its power, with the diverted power
becoming a broad spectral component that could be mistaken for optical shot
noise. The results are in good agreement with recent models accounting for
correlations between the ground hyperfine states. We discuss implications for
quantum sensing and absolute noise calibration in spin-squeezing and
entanglement detection.
