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\subsection{Simulations}  To measure the infall times of satellites in a cosmological context, we use ELVIS (Exploring the Local Volume in Simulations), a suite of cosmological zoom-in $N$-body simulations that are targeted to modeling the LG \citep{GarrisonKimmel2014}.  ELVIS was run using \textsc{GADGET-3} and \textsc{GADGET-2} \citep{Springel2005e}, with initial conditions generated using \textsc{MUSIC} \citep{HahnAbel2011}, all with \citep{Springel2005e} in a  $\Lambda$CDM cosmology based on WMAP7 \citep{Larson2011}: $\sigma_8=0.801$, $\omegamatter=0.266$, $\omegalambda=0.734$, $n_s=0.963$ and $h=0.71$. Within the zoom-in regions, the particle mass is $1.9\times10^5\msun$ and the Plummer-equivalent force softening is $140\pc$ (comoving at $z>9$, physical at $z<9$).  ELVIS contains 48 dark-matter halos of masses similar to the MW or M31 ($\mvir=1.0-2.8\times10^{12}\msun$), with a median $\rvir\approx300\kpc$. $\rvir\approx300\kpc$, the distance at which observed dwarf galaxies show a transition in their properties.  Halfof these halos  are part of a pair that resemble the masses, distance, and relative velocity of the MW-M31 pair, while the other half are single isolated halos matched in masses to the paired ones. We use all 48 halos, given the lack of strong difference in satellite infall times in the paired versus isolated halos \citep{Wetzel2015}.  ELVIS identifies dark-matter (sub)halos using the six-dimensional halo finder \textsc{rockstar} \citep{Behroozi2013a} and constructs merger trees using the \textsc{consistent-trees} algorithm \citep{Behroozi2013b}.  For each halo that is not a subhalo, halo,  we assign a virial mass, $\mvir$, and radius, $\rvir$, according to \citet{BryanNorman1998}. A ``subhalo'' is a halo whose center is inside $\rvir$ of a (more massive) host halo, and when a (sub)halo first  passes within $\rvir$, it experiences ``first infall'' and  becomes a ``satellite'' and experiences ``virial infall''. ``satellite''.  For each (sub)halo, we compute the peak mass, $\mpeak$, that it reached along the history of its primary progenitor.  In order to matchsubhalos  to observed satellites, we assign $\mstar$ to subhalos based on their $\mpeak$ using the relation from abundance matching in \citet{GarrisonKimmel2014}, which reproduces the observed mass function at $\mstar<10^9\msun$ in the LG if one accounts for observational incompleteness \citep{Tollerud2008, Hargis2014}. %While the relation between $\mstar$ and subhalo $\mpeak$ for dwarf galaxies remains highly uncertain, likely with significant scatter, in this work the relation is important \emph{only} in assigning infall time distributions to satellites in a 1-dex bin of $\mstar$.  %As \citet{Wetzel2015} showed, satellite infall times generally change by $<10-20\%$ over $\sim 1$ dex in $\mstar$.