Fisher matrix for multiple tracers: the information in the cross-spectra
  We derive general expressions for the multi-tracer Fisher matrix, both
assuming that the cross-spectra are constrained by the auto-spectra, and also
allowing for independent degrees of freedom in the cross-spectra. We show that,
just like the ratios of power spectra, the independent degrees of freedom of
the cross-spectra are also not constrained by cosmic variance. Moreover,
whereas the uncertainties in the ratios of power spectra decrease with the
number density of the tracers as $\sim 1/\sqrt{\bar{n}}$, the uncertainties in
the independent degrees of freedom of the cross-spectra decrease even faster,
as $\sim 1/\bar{n}$. We also derive simple expressions for the optimal number
of tracers in a survey.
