## 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

### MSC:

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

### Keywords:

eigenvalue; Wishart matrix
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