Appendices

Let N(µ,σ2) denote a Gaussian distribution with meanµ and variance σ2. Let χ2(n) denote a χ2 distribution withn degrees of freedom. Our analysis extensively uses the following facts about Gaussian and χ2 distributions: Definition A.1 (Gaussian and Wigner Random Matrices). We let G N(n) denote an n n randomGaussianmatrixwith i.i.d. We let W W(n)=G+GT denotean n n Wigner matrix, where G N(n). Fact A.1 (χ2 TailBound(Lemma 1of[1])).