On the monotonicity of average singular values of complex Gaussian random matrices

Abstract

We give an alternate proof of the fact that the average singular value of complex Gaussian random matrix decreases with dimension. Conjectured by Bandeira, Kennedy, and Singer (Math. Program., 2016), this property was recently established by Hutn\'ık, for non-negative integer shape parameter $\alpha$. We also extend this monotonicity to real $\alpha \ge 0$.