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arXiv · 2201.00284

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

Cosme Louart
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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 $Q = (I_p - \frac{1}{n}XX^T) ^{-1}$ 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 $X$.

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Cosme Louart. 2022-01-02. Sharp Bounds for the Concentration of the Resolvent in Convex Concentration Settings. https://arxiv.org/abs/2201.00284

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