Under the Gaussian assumption, , so the coincident normally ordered density correlation is . For a homogeneous nonzero density , the large-separation limit is , giving
These coincident-point bunching factors describe enhanced bosonic coincidence and excluded same-component fermionic coincidence. More generally the density-normalized ratio tends to one at large separation. The unnormalized ratio printed in the paper additionally needs matching nonzero local and remote densities; alone does not ensure this. For a bosonic Fock product state, the local normalized value instead is , and even a large-separation factorization must be checked separately.