The Smallest Eigenvalue of a Large Dimensional Wishart Matrix

For positive integers $s, n$ let Mₛ = (1/s)VₛVTₛ, where Vₛ is an n × s matrix composed of i.i.d. $N(0, 1)$ random variables. Assume $n = n(s)$ and n/s → y ∈ (0, 1) as s → ∞. Then it is shown that the smallest eigenvalue of Mₛ converges almost surely to (1 - √ y)² as s → ∞.