The Frequency of Dwarf Galaxy Multiples at Low Redshift in SDSS vs.
  Cosmological Expectations
  We quantify the frequency of companions of low redshift ($0.013 < z <
0.0252$), dwarf galaxies ($2 \times 10^8$ M$_\odot <$ M$_{*} < 5 \times 10^9$
M$_\odot$) that are isolated from more massive galaxies in SDSS and compare
against cosmological expectations using mock observations of the Illustris
simulation. Dwarf multiples are defined as 2 or more dwarfs that have angular
separations > 55'', projected separations r$_p < 150$ kpc and relative
line-of-sight velocities $\Delta V_{\rm LOS} < 150$ km/s. While the mock
catalogs predict a factor of 2 more isolated dwarfs than observed in SDSS, the
mean number of observed companions per dwarf is $N_c \sim 0.04$, in good
agreement with Illustris when accounting for SDSS sensitivity limits. Removing
these limits in the mock catalogs predicts $N_c\sim 0.06$ for future surveys
(LSST, DESI), which will be complete to M$_* = 2\times 10^8$ M$_\odot$. The 3D
separations of mock dwarf multiples reveal a contamination fraction of
$\sim$40% in observations from projection effects. Most isolated multiples are
pairs; triples are rare and it is cosmologically improbable that bound groups
of dwarfs with more than 3 members exist within the parameter range probed in
this study. We find that $<$1% of LMC-analogs in the field have an SMC-analog
companion. The fraction of dwarf "Major Pairs'' (stellar mass ratio $>$1:4)
steadily increases with decreasing Primary stellar mass, whereas the
cosmological "Major Merger rate'' (per Gyr) has the opposite behaviour. We
conclude that cosmological simulations can be reliably used to constrain the
fraction of dwarf mergers across cosmic time.
