The smallest eigenvalue of a large dimensional Wishart matrix. (English) Zbl 0591.60025

Let \(s\to \infty\) and \(n\to \infty\) such that n/s\(\to y\), a number strictly between 0 and 1. It is shown that the smallest eigenvalue of the (random) Wishart matrix \(W(I_ n,s)\) converges a.e. to \((1-y^{1/2})^ 2\) when s tends to infinity. The proof relies strongly on the fact that the entries of \(W(I_ n,s)\) are i.i.d. normal.
Reviewer: Ch.Hipp


60F15 Strong limit theorems
62H99 Multivariate analysis
15B52 Random matrices (algebraic aspects)
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