  The two point correlation function (2PCF) is a powerful statistical tool to
measure galaxy clustering. Although 2PCF has also been used to study the
clustering of stars on parsec and sub-parsec scales, its physical implication
is not clear on such non-linear scales. In this study, we use the
Illustris-TNG50 simulation to study the connection between the 2PCF signals of
accreted halo stars and the assembly histories of Milky Way-mass galaxies. We
find, in general, the 2PCF signal increases with the increase in galactocentric
radii, $r$, and with the decrease in the pair separations. Galaxies which
assemble late on average have stronger 2PCF signals. With $z_{1/4}$, $z_{1/2}$
and $z_{3/4}$ defined as the redshifts when galaxies accreted one-fourth, half
and three-fourths of their ex-situ stellar mass at today, we find all of them
show the strongest correlations with the 2PCF signals at $r\sim0.2R_{200}$.
$z_{3/4}$ shows the strongest correlations at all radii than those of $z_{1/4}$
or $z_{1/2}$, as later accreted stars preserve better clusterings. However, the
correlations between the 2PCF signals at different radii and the galaxy
formation times all have large scatters. The 2PCFs in velocity space show
weaker correlations with the galaxy formation times within $0.38R_{200}$ than
real space 2PCFs, and the scatter is considerably large. Both the real and
velocity space 2PCFs correlate with the assembly histories of the host dark
matter halos as well. Within $0.38R_{200}$, the real space 2PCF shows stronger
correlations with the galaxy formation histories than with the halo formation
histories, while the velocity space 2PCFs do not show large differences. We
conclude that it is difficult to use 2PCF alone to precisely predict the
formation times or assembly histories of galaxies.
