\label{sec:stellar_mass}
Our goal is to map luminous galaxies to the dark-matter (sub)halos in ELVIS. The relation between stellar mass and (sub)halo mass (or maximum circular velocity) for dwarf galaxies is highly uncertain, likely with significant scatter. This is especially true for our lowest-mass subhalos that (likely) host faint and ultra-faint galaxies; some of these subhalos may not host any luminous galaxies, a manifestation of the long-standing “missing satellites problem” \citep{Klypin1999}. Nonetheless, we use the relation from abundance matching to ELVIS (sub)halos in \citet{GarrisonKimmel2014}. This relation is based on that of \citet{Behroozi2013c} but is modified at the low-mass end according to the observed stellar-mass function of \citet{Baldry2012}. This modification better reproduces the dwarf galaxy population (\({M_{\rm star}}< 10 ^ 9 {~\mbox{M}_\odot}\)) of the LG in ELVIS \citep{GarrisonKimmel2014}. At these mass scales, \({M_{\rm star}}\propto {M_{\rm peak}}^ {1.92}\). When possible, we show results as a function of both \({M_{\rm star}}\) and \({M_{\rm peak}}\), given the uncertainties of abundance matching at these low masses.
In selecting the stellar-mass ratio for defining “major” groups or mergers in the histories of dwarf galaxies in Sections \ref{sec:preprocessing_v_mass} and \ref{sec:mergers}, we assume that the slope (but not necessarily normalization) of this relation does not evolve, motivated by the lack of strong evolution observed for slightly more massive galaxies \citep[for example,][]{Leauthaud2012,Hudson2013}, in addition to the lack of observational evidence to suggest otherwise. We define major mergers as those for which the stellar-mass ratio is greater than 0.1. This broadly corresponds to mass ratios at which the lower-mass companion is likely to have significant dynamical effect on the more massive galaxy \citep[for example,][]{Hopkins2010,Helmi2012,YozinBekki2012} and for which recent mergers are likely to be observable. Given our relation between stellar and (sub)halo mass, this corresponds to \({M_{\rm peak}}\) ratios \(\gtrsim 0.3\).