ConKer: evaluating isotropic correlations of arbitrary order
  High order correlations in the cosmic matter density have become increasingly
valuable in cosmological analyses. However, computing such correlation
functions is computationally expensive. We aim to circumvent these challenges
by designing a new method of estimating correlation functions. This is realized
in ConKer, an algorithm that performs FFT convolutions of matter distributions
with spherical kernels. ConKer is applied to the CMASS sample of the SDSS DR12
galaxy survey and used to compute the isotropic correlation up to correlation
order n = 5. We also compare the n = 2 and n = 3 cases to traditional
algorithms to verify the accuracy of the new method. We perform a timing study
of the algorithm and find that two of the three components of the algorithm are
independent of the catalog size, N, while one component is O(N), which starts
dominating for catalogs larger than 10M objects. For n < 5 the dominant
calculation is O(N^(4/3logN)), where N is the number of the grid cells. For
higher n, the execution time is expected to be dominated by a component with
time complexity O(N^((n+2)/3)). We find ConKer to be a fast and accurate method
of probing high order correlations in the cosmic matter density.
