  We consider anyonic quasiparticles with charge e/2 described by the {\nu} =
1/2 chiral Luttinger liquid, which collide in a Hong-Ou-Mandel-like
interferometer. These colliding anyonic channels can be formally viewed as
hosting Laughlin-like fractional {\nu} = 1/2 quasiparticles. More specifically,
two possible geometries are considered: (i) a two-edge-channel setup where
anyons originate from equilibrium reservoirs; (ii) a four-edge-channel setup
where nonequilibrium anyons arrive at the collider in the form of diluted
beams. For both setups, we calculate the tunneling current and the current
correlations. For setup (i), our results provide analytically exact expressions
for the tunneling current, tunneling-current noise, and cross-correlation
noise, The exact relation between conductance and noise is demonstrated. For
setup (ii), we show that the tunneling current and the generalized Fano factor
[defined in B. Rosenow et al. (2016)] are finite for diluted streams of {\nu} =
1/2 anyons. This is due to the processes where nonequilibrium anyons, supplied
via either source edge, directly tunnel at the central QPC. Thus, to obtain
meaningful results in this case, one should go beyond the so-called time-domain
braiding processes, where nonequilibrium anyons do not tunnel at the collider,
but rather indirectly influence the tunneling by braiding with the
quasiparticle-quasihole pairs created at the collider. This suggests that the
effect of direct tunneling and collisions of diluted anyons in the
Hong-Ou-Mandel interferometer can be important for various observables in
physical quantum-Hall edges at Laughlin filling fractions.
