The stellar mass-halo mass relation is a key constraint in all semi-analytic , numerical , and semi-empirical models of galaxy formation and evolution .
However , its exact shape and redshift dependence remain debated .
Several recent works support a relation in the local Universe steeper than previously thought .
Based on the comparisons with a variety of data on massive central galaxies , we show that this steepening holds up to z \sim 1 , for stellar masses M _ { star } \gtrsim 2 \times 10 ^ { 11 } M _ { \odot } .
Specifically , we find significant evidence for a high-mass end slope of \beta \gtrsim 0.35 - 0.70 , instead of the usual \beta \lesssim 0.20 - 0.30 reported by a number of previous results .
When including the independent constraints from the recent BOSS clustering measurements , the data , independent of any systematic errors in stellar masses , tend to favor a model with a very small scatter ( \lesssim 0.15 dex ) in stellar mass at fixed halo mass , in the redshift range z < 0.8 and for M _ { star } > 3 \times 10 ^ { 11 } M _ { \odot } , suggesting a close connection between massive galaxies and host halos even at relatively recent epochs .
We discuss the implications of our results with respect to the evolution of the most massive galaxies since z \sim 1 .