Solution Sheet III

Abstract

1 Limiting density forXX t random matrices Let X = (xij)i∈[M ],j∈[N ] be a (non-symmetric) random matrices with M = M(N) ≤ N , and independent, identically distributed entries xij ∈ R, E xij = 0, E xij = 1, |xij | ≤ C. The symmetric random matrixH = N−1XXt ∈ RM×M then has real eigenvalues λ1 ≤ · · · ≤ λM . The goal of this exercise is to show that in the… (More)

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