The Flatness of Mass-to-Light Ratio on Large Scales

It has been suggested that the mass-to-light ($M/L$) ratio of gravitationally clustering objects is scale-independent on scales beyond galaxy clusters, and may also be independent of the mass of the objects. In this paper, we show that the scale behavior of $M/L$ ratio is closely related to the scaling of cosmic structures larger than clusters. The scale dependence of the $M/L$ ratio can be determined by comparing the observed scaling of richness function (RF) of multi-scale identified objects with the model-predicted scaling of mass function (MF) of large scale structures. Using the multi-scale identified clusters from IRAS 1.2 Jy galaxy survey, we have made comparisons of the observed RF scaling of IRAS $r_{cl}$-clusters with the MF scalings given by simulations of three popular models SCDM, LCDM and OCDM. We find that, the M/L ratio basically is scale-independent from the Abell radius up to about 24 $h^{-1}$Mpc, while it seems to show a slight, but systematical, increase over this scale range. This result is weakly dependent on the cosmological parameters.Comment: AAS Latex file, 8 pages+ 4 figures, accepted for publication in ApJ

On Gaussian Comparison Inequality and Its Application to Spectral Analysis of Large Random Matrices

Recently, Chernozhukov, Chetverikov, and Kato [Ann. Statist. 42 (2014) 1564--1597] developed a new Gaussian comparison inequality for approximating the suprema of empirical processes. This paper exploits this technique to devise sharp inference on spectra of large random matrices. In particular, we show that two long-standing problems in random matrix theory can be solved: (i) simple bootstrap inference on sample eigenvalues when true eigenvalues are tied; (ii) conducting two-sample Roy's covariance test in high dimensions. To establish the asymptotic results, a generalized $\epsilon$-net argument regarding the matrix rescaled spectral norm and several new empirical process bounds are developed and of independent interest.Comment: to appear in Bernoull