Disconnected Covariance of 2-point Functions in Large-Scale Structure
  Optimal analyses using the 2-point functions of large-scale structure probes
require accurate covariance matrices. A covariance matrix of the 2-point
function comprises the disconnected part and the connected part. While the
connected covariance only becomes important on small scales, the disconnected
covariance is dominant on large scales, where the survey window has a
significant impact. In this work, we develop an analytical method to compute
the disconnected covariance, accounting for the window effect. Derived under
the flat-sky approximation, our formalism is applicable to wide surveys by
swapping in the curved-sky window functions. Our method works for both the
power spectrum and the correlation function, and applies to the covariances of
various probes including the multipoles and the wedges of 3D clustering, the
angular and the projected statistics of clustering and shear, as well as the
cross covariances between different probes. We verify the analytic covariance
against the sample covariance from the galaxy mock simulations in two test
cases: (1) the power spectrum multipole covariance, and (2) the joint
covariance of the projected correlation function and the correlation function
multipoles. Our method achieve good agreement with the mocks, while at a
negligible computational cost. Unlike mocks, our analytic covariance is free of
sampling noise, which often leads to numerical problems and the need to inflate
the errors. In addition, our method can use the best-fit power spectrum as
input, in contrast to the standard procedure of using a fiducial model that may
deviate significantly from the truth. We also show that a naive diagonal power
spectrum covariance underestimates the signal-to-noise ratio compared to our
analytic covariance. The code that accompanies this paper is available at
https://github.com/eelregit/covdisc.
