  The Local Group (LG) of galaxies is dominated by the M31 and Milky Way (MW)
pair, a configuration which suggests that the mass distribution in the LG and
its surroundings should be highly anisotropic. We use the APOSTLE cosmological
simulations to examine how this anisotropy manifests on the spatial
distribution and kinematics of dwarf galaxies out to a distance of 3 Mpc from
the MW. The simulations indicate a clear preference for dwarfs to be located
close to the axis defined by the MW-M31 direction, even for dwarfs in the LG
periphery (LGP; i.e., those at distances 1.25<d/Mpc<3). The LGP "Hubble flow"
is also affected; at fixed distance from the MW the mean recession speed,
<V_{rad} >, varies with angular distance to M31, peaking in the anti-M31
direction and reaching a minimum behind M31. The combined M31-MW mass
decelerates the local expansion; the LG "turnaround radius" (where <V_{rad}>=0)
in APOSTLE is located at r ~ 1.25 Mpc from the LG barycentre and the pure
Hubble flow (where <V_{rad}> ~ H_0*d) is not reached out to at least 3 Mpc. The
predicted flow is very cold, with a barycentric dispersion of <40 km/s. A
comparison of these predicted features with existing observations gives mixed
results. There is clear observational evidence for an angular anisotropy in
V_{rad} around the LGP, but little evidence for a preferred spatial
distribution of LGP dwarfs along the MW-M31 axis. The observed local Hubble
flow is also peculiar. Although the coldness of the flow is consistent with the
simulations, it is significantly less decelerated: relative to the MW, on
average, all galaxies beyond d~1.25 Mpc seem to be on a pure Hubble flow. We
argue that these oddities may result from incompleteness and inhomogeneous sky
coverage, but a full explanation may need to await the completion of deep
all-sky surveys able to fill the gaps in our current inventory of nearby
dwarfs.
