We study the evolution of the luminosity-to-halo mass relation of Luminous Red Galaxies (LRGs). We select a sample of 52 000 LOWZ and CMASS LRGs from the Baryon Oscillation Spectroscopic Survey (BOSS) SDSS-DR10 in the ~450 deg^2 that overlaps with imaging data from the second Red-sequence Cluster Survey (RCS2), group them into bins of absolute magnitude and redshift and measure their weak lensing signals. The source redshift distribution has a median of 0.7, which allows us to study the lensing signal as a function of lens redshift. We interpret the lensing signal using a halo model, from which we obtain the halo masses as well as the normalisations of the mass-concentration relations. We find that the concentration of haloes that host LRGs is consistent with dark matter only simulations once we allow for miscentering or satellites in the modelling. The slope of the luminosity-to-halo mass relation has a typical value of 1.4 and does not change with redshift, but we do find evidence for a change in amplitude: the average halo mass of LOWZ galaxies increases by 25_{-14}^{+16} % between z=0.36 and 0.22 to an average value of 6.43+/-0.52 x 10^13 h70^-1 Msun. If we extend the redshift range using the CMASS galaxies and assume that they are the progenitors of the LOWZ sample, we find that the average mass of LRGs increases by 80^{+39}_{-28} % between z=0.6 and 0.2
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