  The kinematics of the Milky Way (MW) and M31, the dominant galaxies in the
Local Group (LG), can be used to estimate the LG total mass. New results on the
M31 proper motion have recently been used to improve that estimate. Those
results are based on kinematic priors that are sometimes guided and evaluated
using cosmological N-body simulations. However, the kinematic properties of
simulated LG analogues could be biased due to the effective power spectrum
truncation induced by the small size of the parent simulation. Here we explore
the dependence of LG kinematics on the simulation box size to argue that
cosmological simulations need a box size on the order of 1 Gpc in order to
claim convergence on the LG kinematic properties. Using a large enough
simulation, we find M31 tangential and radial velocities relative to the MW to
be in the range $v_{\mathrm {tan}}=105^{+94}_{-59} $ km/s and $v_{\mathrm
{rad}}=-108^{+68}_{-81}$ km/s, respectively. This study highlights that LG
kinematics derived from N-body simulations have to be carefully interpreted
taking into account the size of the parent simulation.
