We study the role of major and minor mergers in the mass growth of luminous red galaxies. We present small-scale ($0.01<r<8,hMpc$) projected cross-correlation functions of $23043$ luminous early-type galaxies from the Sloan Digital Sky Survey (SDSS) Luminous Red Galaxy (LRG) sample ($0.16<z<0.30$, $MMiapprox -22.75,mag$) with all their companions in the SDSS imaging sample, split into color and luminosity subsamples with $MMi<-18,mag$. We de-project the two-dimensional functions to obtain three-dimensional real-space LRG--galaxy cross-correlation functions for each companion subsample. We find that the cross-correlation functions are not purely power-law and that there is a clear ``one-halo to ``two-halo transition near $1,hMpc$. We convert these results into close pair statistics and estimate the LRG accretion rate from each companion galaxy subsample using timescales from dynamical friction arguments for each subsample of the companions. We find that the accretion onto LRGs is dominated by dry mergers of galaxies more luminous than $Lstar$. We integrate the luminosity accretion rate from mergers over all companion galaxy subsamples and find that LRGs are growing by $[1.7pm 0.1]$ percent per $Gyr$, on average, from merger activity at redshift $zsim 0.25$. This rate is almost certainly an over-estimate because we have assumed that all close pairs are merging as quickly as dynamical friction allows; nonetheless it is on the low side of the panoply of measurements in the literature, and lower than any rate predicted from theory.
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