Sharp Bounds for the Concentration of the Resolvent in Convex Concentration Settings

Abstract

Considering random matrix $X\in {\mathcal{M}}_{p,n}$ with independent columns satisfying the convex concentration properties issued from a famous theorem of Talagrand, we express the linear concentration of the resolvent $Q=(I_p-\frac{1}{n}X{X}^T{)}^{-1}$ around a classical deterministic equivalent with a good observable diameter for the nuclear norm. The general proof relies on a decomposition of the resolvent as a series of powers of $X$.

18p + 4 Appendix + 1 references. arXiv admin note: text overlap with arXiv:2010.09877