  In this work an ensemble of simulated Local Group analogues is used to
constrain the properties of the mass assembly history of the Milky Way (MW) and
Andromeda (M31) galaxies. These objects have been obtained using the
constrained simulation technique, which ensures that simulated LGs live within
a large scale environment akin to the observed one. Our results are compared
against a standard $\Lambda$ Cold Dark Matter ($\Lambda$CDM) series of
simulations which use the same cosmological parameters. This allows us to
single out the effects of the constraints on the results. We find that (a) the
median constrained merging histories for M31 and MW live above the standard
ones at the 1-$\sigma$ level, (b) the median formation time takes place
$\approx$ 0.5 Gyr earlier than unconstrained values, while the latest major
merger happens on average 1.5 Gyr earlier and (c) the probability for both LG
haloes to have experienced their last major merger in the first half of the
history of the Universe is $\approx$ 50% higher for the constrained pairs.
These results have been estimated to be significant at the 99% confidence level
by means of a Kolmogorov-Simirnov test. These results suggest that the
particular environment in which the Milky Way and Andromeda form plays a role
in shaping their properties, and favours earlier formation and last major
merger time values in agreement with other observational and theoretical
considerations.
