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

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