Marchenko–Pastur edges and conditioning

NumericalBeginner⏱ 15 minRandom Matricesmarchenko-pasturcondition numberaspect ratio

Problem

For a sample covariance matrix with true covariance $I_p$ and aspect ratio $\lambda = p/n$ :

Give the bulk edges and the limiting condition number as functions of $\lambda$ .
Tabulate them for $\lambda = 0.01, 0.1, 0.5, 0.9, 0.99$ .
How large must $n$ be, relative to $p$ , for the condition number to be below $2$ ?

Compute the requested quantities and say what they mean. A number without an interpretation is not an answer.

Opening this before you have a real attempt on paper is the fastest way to feel like you understand something you cannot reproduce.

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