Measures of galaxy environment -- II. Rank-ordered mark correlations
  We analyze environmental correlations using mark clustering statistics with the mock galaxy catalogue constructed by Muldrew et al. (Paper I). We find that mark correlation functions are able to detect even a small dependence of galaxy properties on the environment, quantified by the overdensity $1+\delta$, while such a small dependence would be difficult to detect by traditional methods. We then show that rank ordering the marks and using the rank as a weight is a simple way of comparing the correlation signals for different marks. With this we quantify to what extent fixed-aperture overdensities are sensitive to large-scale halo environments, nearest-neighbor overdensities are sensitive to small-scale environments within haloes, and colour is a better tracer of overdensity than is luminosity. 
Ramin A. Skibba, Ravi K. Sheth, Darren J. Croton, Stuart I. Muldrew,   Ummi Abbas, Frazer R. Pearce, Genevieve M. Shattow
astro-ph.CO